#include <bits/stdc++.h>
using namespace std;
long long n, t, p, k, c[60][60], ans;
int main() {
  cin >> n >> t;
  if (t & (t - 1)) return cout << 0, 0;
  while (!(t >> p & 1)) p++;
  p++, n++;
  for (int i = 0; i < 60; i++)
    for (int j = 0; j < 60; j++)
      if (j <= i) c[i][j] = (i && j) ? c[i - 1][j] + c[i - 1][j - 1] : 1;
  for (long long i = 59; i >= 0; i--)
    if ((n >> i & 1) && p - k >= 0) ans += c[i][p - k], k++;
  if (p == k) ans++;
  if (p == 1) ans--;
  cout << ans;
}

### Prompt

Your challenge is to write 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;
long long n, t, p, k, c[60][60], ans;
int main() {
  cin >> n >> t;
  if (t & (t - 1)) return cout << 0, 0;
  while (!(t >> p & 1)) p++;
  p++, n++;
  for (int i = 0; i < 60; i++)
    for (int j = 0; j < 60; j++)
      if (j <= i) c[i][j] = (i && j) ? c[i - 1][j] + c[i - 1][j - 1] : 1;
  for (long long i = 59; i >= 0; i--)
    if ((n >> i & 1) && p - k >= 0) ans += c[i][p - k], k++;
  if (p == k) ans++;
  if (p == 1) ans--;
  cout << ans;
}

```