#include <bits/stdc++.h>
using namespace std;
long long combi[40][40];
pair<long long, long long> pow2(long long n) {
  if (n == 0) return make_pair(-1, 0);
  long long temp = n;
  int i;
  for (i = -1; n > 0; i++) {
    n >>= 1;
  }
  return make_pair(i, temp - (1LL << i));
}
long long f(long long n, long long k) {
  pair<long long, long long> n2 = pow2(n);
  if (n2.first < k || k < 0) return 0;
  return combi[n2.first][k] + f(n2.second, k - 1);
}
int main() {
  for (int i = 0; i < 40; i++) {
    combi[i][0] = 1;
    combi[i][i] = 1;
  }
  for (int i = 1; i < 40; i++) {
    for (int j = 1; j < i; j++) {
      combi[i][j] = combi[i - 1][j - 1] + combi[i - 1][j];
    }
  }
  long long n, k;
  cin >> n >> k;
  pair<long long, long long> n2 = pow2(n + 2);
  pair<long long, long long> k2 = pow2(k);
  if (k2.second != 0 || n2.first <= k2.first) {
    cout << 0;
    return 0;
  }
  k = k2.first;
  long long ans = combi[n2.first][k + 1] + f(n2.second, k);
  if (k == 0) ans--;
  cout << ans;
  return 0;
}

### Prompt

Develop a solution in Cpp to the problem described below:

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 combi[40][40];
pair<long long, long long> pow2(long long n) {
  if (n == 0) return make_pair(-1, 0);
  long long temp = n;
  int i;
  for (i = -1; n > 0; i++) {
    n >>= 1;
  }
  return make_pair(i, temp - (1LL << i));
}
long long f(long long n, long long k) {
  pair<long long, long long> n2 = pow2(n);
  if (n2.first < k || k < 0) return 0;
  return combi[n2.first][k] + f(n2.second, k - 1);
}
int main() {
  for (int i = 0; i < 40; i++) {
    combi[i][0] = 1;
    combi[i][i] = 1;
  }
  for (int i = 1; i < 40; i++) {
    for (int j = 1; j < i; j++) {
      combi[i][j] = combi[i - 1][j - 1] + combi[i - 1][j];
    }
  }
  long long n, k;
  cin >> n >> k;
  pair<long long, long long> n2 = pow2(n + 2);
  pair<long long, long long> k2 = pow2(k);
  if (k2.second != 0 || n2.first <= k2.first) {
    cout << 0;
    return 0;
  }
  k = k2.first;
  long long ans = combi[n2.first][k + 1] + f(n2.second, k);
  if (k == 0) ans--;
  cout << ans;
  return 0;
}

```