#include <bits/stdc++.h>
using namespace std;
const int MAX = 0;
long long n, t, cc[66][66];
long long fnd(long long x, long long y) {
  if (x < 0 || y < 0) return 0;
  if (y > x) return 0;
  if (x == y || y == 0) return 1ll;
  if (cc[x][y] != -1) return cc[x][y];
  return (cc[x][y] = fnd(x - 1, y) + fnd(x - 1, y - 1));
}
int main() {
  cin >> n >> t;
  long long lt = 0;
  n++;
  long long nn = n, tn = 0;
  while (nn > 0) {
    tn += nn % 2;
    nn /= 2;
  }
  while (t > 1) {
    if (t % 2 == 1) {
      cout << 0 << endl;
      return 0;
    }
    t /= 2;
    lt++;
  }
  lt++;
  memset(cc, -1, sizeof cc);
  long long ans = 0, cn = 0, cOne = tn - 1;
  while (n > 0) {
    if (n % 2 == 1) {
      ans += fnd(cn, lt - cOne);
      cerr << fnd(cn, lt - cOne) << endl;
      cerr << cn << "    " << lt - cOne << endl;
    }
    cOne -= n % 2;
    n /= 2;
    cn++;
  }
  if (lt == tn) ans++;
  if (lt == 1)
    cout << ans - 1 << endl;
  else
    cout << ans << endl;
}

### 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 MAX = 0;
long long n, t, cc[66][66];
long long fnd(long long x, long long y) {
  if (x < 0 || y < 0) return 0;
  if (y > x) return 0;
  if (x == y || y == 0) return 1ll;
  if (cc[x][y] != -1) return cc[x][y];
  return (cc[x][y] = fnd(x - 1, y) + fnd(x - 1, y - 1));
}
int main() {
  cin >> n >> t;
  long long lt = 0;
  n++;
  long long nn = n, tn = 0;
  while (nn > 0) {
    tn += nn % 2;
    nn /= 2;
  }
  while (t > 1) {
    if (t % 2 == 1) {
      cout << 0 << endl;
      return 0;
    }
    t /= 2;
    lt++;
  }
  lt++;
  memset(cc, -1, sizeof cc);
  long long ans = 0, cn = 0, cOne = tn - 1;
  while (n > 0) {
    if (n % 2 == 1) {
      ans += fnd(cn, lt - cOne);
      cerr << fnd(cn, lt - cOne) << endl;
      cerr << cn << "    " << lt - cOne << endl;
    }
    cOne -= n % 2;
    n /= 2;
    cn++;
  }
  if (lt == tn) ans++;
  if (lt == 1)
    cout << ans - 1 << endl;
  else
    cout << ans << endl;
}

```