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New data format

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This commit is contained in:
Joseph Redmon 2013-12-06 13:26:09 -08:00
parent b715671988
commit 4bdf96bd6a
12 changed files with 279 additions and 243 deletions
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8
Makefile
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@ -1,5 +1,11 @@
CC=gcc
COMMON=-Wall `pkg-config --cflags opencv` -isystem /usr/local/Cellar/opencv/2.4.6.1/include/opencv -isystem /usr/local/Cellar/opencv/2.4.6.1/include
COMMON=-Wall `pkg-config --cflags opencv`
UNAME = $(shell uname)
ifeq ($(UNAME), Darwin)
COMMON += -isystem /usr/local/Cellar/opencv/2.4.6.1/include/opencv -isystem /usr/local/Cellar/opencv/2.4.6.1/include
else
COMMON += -march=native
endif
CFLAGS= $(COMMON) -O3 -ffast-math -flto
#CFLAGS= $(COMMON) -O0 -g
LDFLAGS=`pkg-config --libs opencv` -lm

1
src/connected_layer.c
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@ -69,7 +69,6 @@ void update_connected_layer(connected_layer layer, double step, double momentum,
int index = i*layer.inputs+j;
layer.weight_momentum[index] = step*(layer.weight_updates[index] - decay*layer.weights[index]) + momentum*layer.weight_momentum[index];
layer.weights[index] += layer.weight_momentum[index];
//layer.weights[index] = constrain(layer.weights[index], 100.);
}
}
memset(layer.bias_updates, 0, layer.outputs*sizeof(double));

13
src/convolutional_layer.c
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@ -143,26 +143,22 @@ void learn_convolutional_layer(convolutional_layer layer, double *input)
for(i = 0; i < layer.n; ++i){
kernel_update(in_image, layer.kernel_updates[i], layer.stride, i, out_delta, layer.edge);
layer.bias_updates[i] += avg_image_layer(out_delta, i);
//printf("%30.20lf\n", layer.bias_updates[i]);
}
}
void update_convolutional_layer(convolutional_layer layer, double step, double momentum, double decay)
{
//step = .01;
int i,j;
for(i = 0; i < layer.n; ++i){
layer.bias_momentum[i] = step*(layer.bias_updates[i])
+ momentum*layer.bias_momentum[i];
layer.biases[i] += layer.bias_momentum[i];
//layer.biases[i] = constrain(layer.biases[i],1.);
layer.bias_updates[i] = 0;
int pixels = layer.kernels[i].h*layer.kernels[i].w*layer.kernels[i].c;
for(j = 0; j < pixels; ++j){
layer.kernel_momentum[i].data[j] = step*(layer.kernel_updates[i].data[j] - decay*layer.kernels[i].data[j])
+ momentum*layer.kernel_momentum[i].data[j];
layer.kernels[i].data[j] += layer.kernel_momentum[i].data[j];
//layer.kernels[i].data[j] = constrain(layer.kernels[i].data[j], 1.);
}
zero_image(layer.kernel_updates[i]);
}
@ -188,14 +184,6 @@ void visualize_convolutional_filters(convolutional_layer layer, char *window)
int w_offset = i*(size+border);
image k = layer.kernels[i];
image copy = copy_image(k);
/*
printf("Kernel %d - Bias: %f, Channels:",i,layer.biases[i]);
for(j = 0; j < k.c; ++j){
double a = avg_image_layer(k, j);
printf("%f, ", a);
}
printf("\n");
*/
normalize_image(copy);
for(j = 0; j < k.c; ++j){
set_pixel(copy,0,0,j,layer.biases[i]);
@ -227,7 +215,6 @@ void visualize_convolutional_layer(convolutional_layer layer)
{
int i;
char buff[256];
//image vis = make_image(layer.n*layer.size, layer.size*layer.kernels[0].c, 3);
for(i = 0; i < layer.n; ++i){
image k = layer.kernels[i];
sprintf(buff, "Kernel %d", i);

179
src/data.c
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@ -1,23 +1,12 @@
#include "data.h"
#include "list.h"
#include "utils.h"
#include "image.h"
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
batch make_batch(int n, int k)
{
batch b;
b.n = n;
if(k < 3) k = 1;
b.images = calloc(n, sizeof(image));
b.truth = calloc(n, sizeof(double *));
int i;
for(i =0 ; i < n; ++i) b.truth[i] = calloc(k, sizeof(double));
return b;
}
list *get_paths(char *filename)
{
char *path;
@ -41,75 +30,145 @@ void fill_truth(char *path, char **labels, int k, double *truth)
}
}
batch load_list(list *paths, char **labels, int k)
{
char *path;
batch data = make_batch(paths->size, 2);
node *n = paths->front;
int i;
for(i = 0; i < data.n; ++i){
path = (char *)n->val;
data.images[i] = load_image(path);
fill_truth(path, labels, k, data.truth[i]);
n = n->next;
}
return data;
}
batch get_all_data(char *filename, char **labels, int k)
{
list *paths = get_paths(filename);
batch b = load_list(paths, labels, k);
free_list_contents(paths);
free_list(paths);
return b;
}
void free_batch(batch b)
data load_data_image_paths(char **paths, int n, char **labels, int k)
{
int i;
for(i = 0; i < b.n; ++i){
free_image(b.images[i]);
free(b.truth[i]);
data d;
d.shallow = 0;
d.X.rows = n;
d.X.vals = calloc(d.X.rows, sizeof(double*));
d.y = make_matrix(n, k);
for(i = 0; i < n; ++i){
image im = load_image(paths[i]);
d.X.vals[i] = im.data;
d.X.cols = im.h*im.w*im.c;
fill_truth(paths[i], labels, k, d.y.vals[i]);
}
free(b.images);
free(b.truth);
return d;
}
batch get_batch(char *filename, int curr, int total, char **labels, int k)
data load_data_image_pathfile(char *filename, char **labels, int k)
{
list *plist = get_paths(filename);
char **paths = (char **)list_to_array(plist);
int i;
int start = curr*plist->size/total;
int end = (curr+1)*plist->size/total;
batch b = make_batch(end-start, 2);
for(i = start; i < end; ++i){
b.images[i-start] = load_image(paths[i]);
fill_truth(paths[i], labels, k, b.truth[i-start]);
}
data d = load_data_image_paths(paths, plist->size, labels, k);
free_list_contents(plist);
free_list(plist);
free(paths);
return b;
return d;
}
batch random_batch(char *filename, int n, char **labels, int k)
void free_data(data d)
{
if(!d.shallow){
free_matrix(d.X);
free_matrix(d.y);
}else{
free(d.X.vals);
free(d.y.vals);
}
}
data load_data_image_pathfile_part(char *filename, int part, int total, char **labels, int k)
{
list *plist = get_paths(filename);
char **paths = (char **)list_to_array(plist);
int start = part*plist->size/total;
int end = (part+1)*plist->size/total;
data d = load_data_image_paths(paths+start, end-start, labels, k);
free_list_contents(plist);
free_list(plist);
free(paths);
return d;
}
data load_data_image_pathfile_random(char *filename, int n, char **labels, int k)
{
int i;
batch b = make_batch(n, 2);
list *plist = get_paths(filename);
char **paths = (char **)list_to_array(plist);
char **random_paths = calloc(n, sizeof(char*));
for(i = 0; i < n; ++i){
int index = rand()%plist->size;
b.images[i] = load_image(paths[index]);
//scale_image(b.images[i], 1./255.);
z_normalize_image(b.images[i]);
fill_truth(paths[index], labels, k, b.truth[i]);
//print_image(b.images[i]);
random_paths[i] = paths[index];
}
data d = load_data_image_paths(random_paths, n, labels, k);
free_list_contents(plist);
free_list(plist);
free(paths);
return b;
free(random_paths);
return d;
}
data load_categorical_data_csv(char *filename, int target, int k)
{
data d;
d.shallow = 0;
matrix X = csv_to_matrix(filename);
double *truth_1d = pop_column(&X, target);
double **truth = one_hot_encode(truth_1d, X.rows, k);
matrix y;
y.rows = X.rows;
y.cols = k;
y.vals = truth;
d.X = X;
d.y = y;
free(truth_1d);
return d;
}
void randomize_data(data d)
{
int i;
for(i = d.X.rows-1; i > 0; --i){
int index = rand()%i;
double *swap = d.X.vals[index];
d.X.vals[index] = d.X.vals[i];
d.X.vals[i] = swap;
swap = d.y.vals[index];
d.y.vals[index] = d.y.vals[i];
d.y.vals[i] = swap;
}
}
void normalize_data_rows(data d)
{
int i;
for(i = 0; i < d.X.rows; ++i){
normalize_array(d.X.vals[i], d.X.cols);
}
}
data *cv_split_data(data d, int part, int total)
{
data *split = calloc(2, sizeof(data));
int i;
int start = part*d.X.rows/total;
int end = (part+1)*d.X.rows/total;
data train;
data test;
train.shallow = test.shallow = 1;
test.X.rows = test.y.rows = end-start;
train.X.rows = train.y.rows = d.X.rows - (end-start);
train.X.cols = test.X.cols = d.X.cols;
train.y.cols = test.y.cols = d.y.cols;
for(i = 0; i < start; ++i){
train.X.vals[i] = d.X.vals[i];
train.y.vals[i] = d.y.vals[i];
}
for(i = start; i < end; ++i){
test.X.vals[i-start] = d.X.vals[i];
test.y.vals[i-start] = d.y.vals[i];
}
for(i = end; i < d.X.rows; ++i){
train.X.vals[i-(start-end)] = d.X.vals[i];
train.y.vals[i-(start-end)] = d.y.vals[i];
}
split[0] = train;
split[1] = test;
return split;
}

24
src/data.h
View File

@ -1,18 +1,24 @@
#ifndef DATA_H
#define DATA_H
#include "image.h"
#include "matrix.h"
typedef struct{
int n;
image *images;
double **truth;
} batch;
matrix X;
matrix y;
int shallow;
} data;
batch get_all_data(char *filename, char **labels, int k);
batch random_batch(char *filename, int n, char **labels, int k);
batch get_batch(char *filename, int curr, int total, char **labels, int k);
void free_batch(batch b);
data load_data_image_pathfile(char *filename, char **labels, int k);
void free_data(data d);
data load_data_image_pathfile(char *filename, char **labels, int k);
data load_data_image_pathfile_part(char *filename, int part, int total,
char **labels, int k);
data load_data_image_pathfile_random(char *filename, int n, char **labels, int k);
data load_categorical_data_csv(char *filename, int target, int k);
void normalize_data_rows(data d);
void randomize_data(data d);
data *cv_split_data(data d, int part, int total);
#endif

11
src/matrix.c
View File

@ -13,6 +13,17 @@ void free_matrix(matrix m)
free(m.vals);
}
void matrix_add_matrix(matrix from, matrix to)
{
assert(from.rows == to.rows && from.cols == to.cols);
int i,j;
for(i = 0; i < from.rows; ++i){
for(j = 0; j < from.cols; ++j){
to.vals[i][j] += from.vals[i][j];
}
}
}
matrix make_matrix(int rows, int cols)
{
matrix m;

95
src/network.c
View File

@ -15,6 +15,8 @@ network make_network(int n)
net.n = n;
net.layers = calloc(net.n, sizeof(void *));
net.types = calloc(net.n, sizeof(LAYER_TYPE));
net.outputs = 0;
net.output = 0;
return net;
}
@ -45,13 +47,13 @@ void forward_network(network net, double *input)
}
}
void update_network(network net, double step)
void update_network(network net, double step, double momentum, double decay)
{
int i;
for(i = 0; i < net.n; ++i){
if(net.types[i] == CONVOLUTIONAL){
convolutional_layer layer = *(convolutional_layer *)net.layers[i];
update_convolutional_layer(layer, step, 0.9, .01);
update_convolutional_layer(layer, step, momentum, decay);
}
else if(net.types[i] == MAXPOOL){
//maxpool_layer layer = *(maxpool_layer *)net.layers[i];
@ -61,7 +63,7 @@ void update_network(network net, double step)
}
else if(net.types[i] == CONNECTED){
connected_layer layer = *(connected_layer *)net.layers[i];
update_connected_layer(layer, step, .9, 0);
update_connected_layer(layer, step, momentum, decay);
}
}
}
@ -111,8 +113,26 @@ double *get_network_delta(network net)
return get_network_delta_layer(net, net.n-1);
}
void learn_network(network net, double *input)
void calculate_error_network(network net, double *truth)
{
double *delta = get_network_delta(net);
double *out = get_network_output(net);
int i, k = get_network_output_size(net);
for(i = 0; i < k; ++i){
delta[i] = truth[i] - out[i];
}
}
int get_predicted_class_network(network net)
{
double *out = get_network_output(net);
int k = get_network_output_size(net);
return max_index(out, k);
}
void backward_network(network net, double *input, double *truth)
{
calculate_error_network(net, truth);
int i;
double *prev_input;
double *prev_delta;
@ -145,40 +165,43 @@ void learn_network(network net, double *input)
}
}
void train_network_batch(network net, batch b)
int train_network_datum(network net, double *x, double *y, double step, double momentum, double decay)
{
int i,j;
int k = get_network_output_size(net);
forward_network(net, x);
int class = get_predicted_class_network(net);
backward_network(net, x, y);
update_network(net, step, momentum, decay);
return (y[class]?1:0);
}
double train_network_sgd(network net, data d, double step, double momentum,double decay)
{
int i;
int correct = 0;
for(i = 0; i < b.n; ++i){
show_image(b.images[i], "Input");
forward_network(net, b.images[i].data);
image o = get_network_image(net);
if(o.h) show_image_collapsed(o, "Output");
double *output = get_network_output(net);
double *delta = get_network_delta(net);
int max_k = 0;
double max = 0;
for(j = 0; j < k; ++j){
delta[j] = b.truth[i][j]-output[j];
if(output[j] > max) {
max = output[j];
max_k = j;
for(i = 0; i < d.X.rows; ++i){
int index = rand()%d.X.rows;
correct += train_network_datum(net, d.X.vals[index], d.y.vals[index], step, momentum, decay);
if((i+1)%10 == 0){
printf("%d: %f\n", (i+1), (double)correct/(i+1));
}
}
if(b.truth[i][max_k]) ++correct;
printf("%f\n", (double)correct/(i+1));
learn_network(net, b.images[i].data);
update_network(net, .001);
return (double)correct/d.X.rows;
}
void train_network(network net, data d, double step, double momentum, double decay)
{
int i;
int correct = 0;
for(i = 0; i < d.X.rows; ++i){
correct += train_network_datum(net, d.X.vals[i], d.y.vals[i], step, momentum, decay);
if(i%100 == 0){
visualize_network(net);
cvWaitKey(100);
cvWaitKey(10);
}
}
visualize_network(net);
print_network(net);
cvWaitKey(100);
printf("Accuracy: %f\n", (double)correct/b.n);
printf("Accuracy: %f\n", (double)correct/d.X.rows);
}
int get_network_output_size_layer(network net, int i)
@ -250,7 +273,7 @@ void print_network(network net)
{
int i,j;
for(i = 0; i < net.n; ++i){
double *output;
double *output = 0;
int n = 0;
if(net.types[i] == CONVOLUTIONAL){
convolutional_layer layer = *(convolutional_layer *)net.layers[i];
@ -283,3 +306,17 @@ void print_network(network net)
fprintf(stderr, "\n");
}
}
double network_accuracy(network net, data d)
{
int i;
int correct = 0;
int k = get_network_output_size(net);
for(i = 0; i < d.X.rows; ++i){
forward_network(net, d.X.vals[i]);
double *out = get_network_output(net);
int guess = max_index(out, k);
if(d.y.vals[i][guess]) ++correct;
}
return (double)correct/d.X.rows;
}

11
src/network.h
View File

@ -16,13 +16,17 @@ typedef struct {
int n;
void **layers;
LAYER_TYPE *types;
int outputs;
double *output;
} network;
network make_network(int n);
void forward_network(network net, double *input);
void learn_network(network net, double *input);
void update_network(network net, double step);
void train_network_batch(network net, batch b);
void backward_network(network net, double *input, double *truth);
void update_network(network net, double step, double momentum, double decay);
double train_network_sgd(network net, data d, double step, double momentum,double decay);
void train_network(network net, data d, double step, double momentum, double decay);
double network_accuracy(network net, data d);
double *get_network_output(network net);
double *get_network_output_layer(network net, int i);
double *get_network_delta_layer(network net, int i);
@ -31,6 +35,7 @@ int get_network_output_size_layer(network net, int i);
int get_network_output_size(network net);
image get_network_image(network net);
image get_network_image_layer(network net, int i);
int get_predicted_class_network(network net);
void print_network(network net);
void visualize_network(network net);

2
src/parser.c
View File

@ -107,6 +107,8 @@ network parse_network_cfg(char *filename)
++count;
n = n->next;
}
net.outputs = get_network_output_size(net);
net.output = get_network_output(net);
return net;
}

156
src/tests.c
View File

@ -166,19 +166,16 @@ void test_parser()
avgerr = .99 * avgerr + .01 * err;
if(count % 1000000 == 0) printf("%f %f :%f AVG %f \n", truth, out[0], err, avgerr);
delta[0] = truth - out[0];
learn_network(net, input);
update_network(net, .001);
backward_network(net, input, &truth);
update_network(net, .001,0,0);
}
}
void test_data()
{
char *labels[] = {"cat","dog"};
batch train = random_batch("train_paths.txt", 101,labels, 2);
show_image(train.images[0], "Test Data Loading");
show_image(train.images[100], "Test Data Loading");
show_image(train.images[10], "Test Data Loading");
free_batch(train);
data train = load_data_image_pathfile_random("train_paths.txt", 101,labels, 2);
free_data(train);
}
void test_full()
@ -188,110 +185,37 @@ void test_full()
int i = 0;
char *labels[] = {"cat","dog"};
while(i++ < 1000 || 1){
batch train = random_batch("train_paths.txt", 1000, labels, 2);
train_network_batch(net, train);
free_batch(train);
data train = load_data_image_pathfile_random("train_paths.txt", 1000, labels, 2);
train_network(net, train, .0005, 0, 0);
free_data(train);
printf("Round %d\n", i);
}
}
double error_network(network net, matrix m, double **truth)
{
int i;
int correct = 0;
int k = get_network_output_size(net);
for(i = 0; i < m.rows; ++i){
forward_network(net, m.vals[i]);
double *out = get_network_output(net);
int guess = max_index(out, k);
if(truth[i][guess]) ++correct;
}
return (double)correct/m.rows;
}
double **one_hot(double *a, int n, int k)
{
int i;
double **t = calloc(n, sizeof(double*));
for(i = 0; i < n; ++i){
t[i] = calloc(k, sizeof(double));
int index = (int)a[i];
t[i][index] = 1;
}
return t;
}
void test_nist()
{
srand(999999);
srand(444444);
network net = parse_network_cfg("nist.cfg");
matrix m = csv_to_matrix("mnist/mnist_train.csv");
matrix test = csv_to_matrix("mnist/mnist_test.csv");
double *truth_1d = pop_column(&m, 0);
double **truth = one_hot(truth_1d, m.rows, 10);
double *test_truth_1d = pop_column(&test, 0);
double **test_truth = one_hot(test_truth_1d, test.rows, 10);
int i,j;
clock_t start = clock(), end;
for(i = 0; i < test.rows; ++i){
normalize_array(test.vals[i], 28*28);
//scale_array(m.vals[i], 28*28, 1./255.);
//translate_array(m.vals[i], 28*28, -.1);
}
for(i = 0; i < m.rows; ++i){
normalize_array(m.vals[i], 28*28);
//scale_array(m.vals[i], 28*28, 1./255.);
//translate_array(m.vals[i], 28*28, -.1);
}
data train = load_categorical_data_csv("mnist/mnist_train.csv", 0, 10);
data test = load_categorical_data_csv("mnist/mnist_test.csv",0,10);
normalize_data_rows(train);
normalize_data_rows(test);
randomize_data(train);
int count = 0;
double lr = .0005;
while(++count <= 300){
//lr *= .99;
int index = 0;
int correct = 0;
int number = 1000;
for(i = 0; i < number; ++i){
index = rand()%m.rows;
forward_network(net, m.vals[index]);
double *out = get_network_output(net);
double *delta = get_network_delta(net);
int max_i = 0;
double max = out[0];
for(j = 0; j < 10; ++j){
delta[j] = truth[index][j]-out[j];
if(out[j] > max){
max = out[j];
max_i = j;
while(++count <= 1){
double acc = train_network_sgd(net, train, lr, .9, .001);
printf("Training Accuracy: %lf", acc);
lr /= 2;
}
}
if(truth[index][max_i]) ++correct;
learn_network(net, m.vals[index]);
update_network(net, lr);
}
print_network(net);
image input = double_to_image(28,28,1, m.vals[index]);
//show_image(input, "Input");
image o = get_network_image(net);
//show_image_collapsed(o, "Output");
visualize_network(net);
cvWaitKey(10);
//double test_acc = error_network(net, m, truth);
fprintf(stderr, "\n%5d: %f %f\n\n",count, (double)correct/number, lr);
if(count % 10 == 0 && 0){
double train_acc = error_network(net, m, truth);
/*
double train_acc = network_accuracy(net, train);
fprintf(stderr, "\nTRAIN: %f\n", train_acc);
double test_acc = error_network(net, test, test_truth);
double test_acc = network_accuracy(net, test);
fprintf(stderr, "TEST: %f\n\n", test_acc);
printf("%d, %f, %f\n", count, train_acc, test_acc);
}
if(count % (m.rows/number) == 0) lr /= 2;
}
double train_acc = error_network(net, m, truth);
fprintf(stderr, "\nTRAIN: %f\n", train_acc);
double test_acc = error_network(net, test, test_truth);
fprintf(stderr, "TEST: %f\n\n", test_acc);
printf("%d, %f, %f\n", count, train_acc, test_acc);
end = clock();
*/
//end = clock();
//printf("Neural Net Learning: %lf seconds\n", (double)(end-start)/CLOCKS_PER_SEC);
}
@ -315,9 +239,9 @@ void test_random_classify()
{
network net = parse_network_cfg("connected.cfg");
matrix m = csv_to_matrix("train.csv");
matrix ho = hold_out_matrix(&m, 2500);
//matrix ho = hold_out_matrix(&m, 2500);
double *truth = pop_column(&m, 0);
double *ho_truth = pop_column(&ho, 0);
//double *ho_truth = pop_column(&ho, 0);
int i;
clock_t start = clock(), end;
int count = 0;
@ -333,8 +257,8 @@ void test_random_classify()
delta[0] = truth[index] - out[0];
// printf("%f\n", delta[0]);
//printf("%f %f\n", truth[index], out[0]);
learn_network(net, m.vals[index]);
update_network(net, .00001);
//backward_network(net, m.vals[index], );
update_network(net, .00001, 0,0);
}
//double test_acc = error_network(net, m, truth);
//double valid_acc = error_network(net, ho, ho_truth);
@ -356,33 +280,19 @@ void test_random_classify()
printf("Neural Net Learning: %lf seconds\n", (double)(end-start)/CLOCKS_PER_SEC);
}
void test_random_preprocess()
void test_split()
{
FILE *file = fopen("train.csv", "w");
char *labels[] = {"cat","dog"};
int i,j,k;
srand(0);
network net = parse_network_cfg("convolutional.cfg");
for(i = 0; i < 100; ++i){
printf("%d\n", i);
batch part = get_batch("train_paths.txt", i, 100, labels, 2);
for(j = 0; j < part.n; ++j){
forward_network(net, part.images[j].data);
double *out = get_network_output(net);
fprintf(file, "%f", part.truth[j][0]);
for(k = 0; k < get_network_output_size(net); ++k){
fprintf(file, ",%f", out[k]);
}
fprintf(file, "\n");
}
free_batch(part);
}
data train = load_categorical_data_csv("mnist/mnist_train.csv", 0, 10);
data *split = cv_split_data(train, 0, 13);
printf("%d, %d, %d\n", train.X.rows, split[0].X.rows, split[1].X.rows);
}
int main()
{
//test_kernel_update();
test_nist();
test_split();
// test_nist();
//test_full();
//test_random_preprocess();
//test_random_classify();

13
src/utils.c
View File

@ -216,3 +216,16 @@ double rand_normal()
for(i = 0; i < 12; ++i) sum += (double)rand()/RAND_MAX;
return sum-6.;
}
double **one_hot_encode(double *a, int n, int k)
{
int i;
double **t = calloc(n, sizeof(double*));
for(i = 0; i < n; ++i){
t[i] = calloc(k, sizeof(double));
int index = (int)a[i];
t[i][index] = 1;
}
return t;
}

1
src/utils.h
View File

@ -22,5 +22,6 @@ double constrain(double a, double max);
double rand_normal();
double mean_array(double *a, int n);
double variance_array(double *a, int n);
double **one_hot_encode(double *a, int n, int k);
#endif