#include <bits/stdc++.h>
long long c[41][41];
long long n, t, sol;
int main(void) {
  scanf("%I64D%I64d", &n, &t);
  if (t & (t - 1)) {
    printf("0\n");
    return 0;
  }
  for (int i = 0; i <= 40; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++) c[i][j] = c[i - 1][j - 1] + c[i - 1][j];
  }
  int pot = 0;
  for (; (1ll << pot) < t; pot++)
    ;
  pot++;
  n += 2;
  int k = 0;
  for (int i = 40; i >= 0 && k <= pot; i--)
    if ((1ll << i) & n) {
      sol += c[i][pot - k];
      k++;
    }
  if (pot == 1) sol--;
  printf("%I64d\n", sol);
  return 0;
}

### Prompt

Please formulate 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>
long long c[41][41];
long long n, t, sol;
int main(void) {
  scanf("%I64D%I64d", &n, &t);
  if (t & (t - 1)) {
    printf("0\n");
    return 0;
  }
  for (int i = 0; i <= 40; i++) {
    c[i][0] = 1;
    for (int j = 1; j <= i; j++) c[i][j] = c[i - 1][j - 1] + c[i - 1][j];
  }
  int pot = 0;
  for (; (1ll << pot) < t; pot++)
    ;
  pot++;
  n += 2;
  int k = 0;
  for (int i = 40; i >= 0 && k <= pot; i--)
    if ((1ll << i) & n) {
      sol += c[i][pot - k];
      k++;
    }
  if (pot == 1) sol--;
  printf("%I64d\n", sol);
  return 0;
}

```