#include <bits/stdc++.h>
using namespace std;
const int SZ = 42;
long long N, T;
int K, Q;
long long Len[SZ + 10];
long long Table[SZ + 5][SZ + 5];
long long res;
int main() {
  int i, j, k;
  scanf("%I64d%I64d", &N, &T);
  for (K = 0; (1ll << K) < T; K++)
    ;
  if ((1ll << K) != T) {
    puts("0");
    return 0;
  }
  Len[1] = 2;
  for (i = 2; i <= SZ; i++) Len[i] = Len[i - 1] * 3 - Len[i - 2] * 2;
  Table[0][0] = Table[1][0] = Table[1][1] = 1;
  for (i = 2; i <= SZ; i++) {
    for (j = 0; j <= SZ; j++) Table[i][j] += Table[i - 1][j];
    for (j = 1; j <= SZ; j++) Table[i][j] += Table[i - 1][j - 1];
  }
  for (i = SZ, k = 0; i > 0 && N > 0; i--) {
    if (Len[i] <= N) {
      for (k = 1; k <= i; k++) res += Table[k][K];
      Q = i;
      N -= Len[i];
      break;
    }
  }
  for (i = Q, k = 0; i >= 0; i--) {
    if (N & (1ll << i)) {
      res += Table[i][K - k];
      ++k;
    }
  }
  printf("%I64d\n", res);
  return 0;
}

### Prompt

Your task is to create a CPP solution to the following problem:

Maxim loves to fill in a matrix in a special manner. Here is a pseudocode of filling in a matrix of size (m + 1) × (m + 1):

<image>

Maxim asks you to count, how many numbers m (1 ≤ m ≤ n) are there, such that the sum of values in the cells in the row number m + 1 of the resulting matrix equals t.

Expression (x xor y) means applying the operation of bitwise excluding "OR" to numbers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by character "^", in Pascal — by "xor".

Input

A single line contains two integers n and t (1 ≤ n, t ≤ 1012, t ≤ n + 1).

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

In a single line print a single integer — the answer to the problem. 

Examples

Input

1 1


Output

1


Input

3 2


Output

1


Input

3 3


Output

0


Input

1000000000000 1048576


Output

118606527258

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int SZ = 42;
long long N, T;
int K, Q;
long long Len[SZ + 10];
long long Table[SZ + 5][SZ + 5];
long long res;
int main() {
  int i, j, k;
  scanf("%I64d%I64d", &N, &T);
  for (K = 0; (1ll << K) < T; K++)
    ;
  if ((1ll << K) != T) {
    puts("0");
    return 0;
  }
  Len[1] = 2;
  for (i = 2; i <= SZ; i++) Len[i] = Len[i - 1] * 3 - Len[i - 2] * 2;
  Table[0][0] = Table[1][0] = Table[1][1] = 1;
  for (i = 2; i <= SZ; i++) {
    for (j = 0; j <= SZ; j++) Table[i][j] += Table[i - 1][j];
    for (j = 1; j <= SZ; j++) Table[i][j] += Table[i - 1][j - 1];
  }
  for (i = SZ, k = 0; i > 0 && N > 0; i--) {
    if (Len[i] <= N) {
      for (k = 1; k <= i; k++) res += Table[k][K];
      Q = i;
      N -= Len[i];
      break;
    }
  }
  for (i = Q, k = 0; i >= 0; i--) {
    if (N & (1ll << i)) {
      res += Table[i][K - k];
      ++k;
    }
  }
  printf("%I64d\n", res);
  return 0;
}

```