#include <bits/stdc++.h>
using namespace std;
bool flag;
long long List[41], F[41][41], N, T, Ct, Ans, A[41], Cnt;
void Solve() {
  for (int i = 1; i <= 40; ++i) {
    if (N >= List[i])
      N -= List[i], Ans += F[i][Ct];
    else
      break;
  }
  while (N) {
    A[++Cnt] = N % 2;
    N /= 2;
  }
  int j = 0;
  for (int i = Cnt; i >= 1; --i)
    if (A[i] && Ct >= j) {
      Ans += F[i - 1][Ct - j];
      ++j;
    }
  cout << Ans << endl;
}
void Prework() {
  List[0] = 1;
  for (int i = 1; i <= 40; ++i) List[i] = List[i - 1] * 2;
  F[0][0] = 1;
  for (int i = 1; i <= 40; ++i) {
    F[i][0] = 1;
    for (int j = 1; j <= i; ++j) F[i][j] = F[i - 1][j - 1] + F[i - 1][j];
  }
  for (int i = 0; i <= 40; ++i) {
    if (List[i] == T)
      Ct = i, flag = true;
    else if (List[i] > T)
      break;
  }
}
int main() {
  cin >> N >> T;
  Prework();
  if (!flag)
    cout << 0 << endl;
  else
    Solve();
  return 0;
}

### Prompt

Create a solution in Cpp for 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;
bool flag;
long long List[41], F[41][41], N, T, Ct, Ans, A[41], Cnt;
void Solve() {
  for (int i = 1; i <= 40; ++i) {
    if (N >= List[i])
      N -= List[i], Ans += F[i][Ct];
    else
      break;
  }
  while (N) {
    A[++Cnt] = N % 2;
    N /= 2;
  }
  int j = 0;
  for (int i = Cnt; i >= 1; --i)
    if (A[i] && Ct >= j) {
      Ans += F[i - 1][Ct - j];
      ++j;
    }
  cout << Ans << endl;
}
void Prework() {
  List[0] = 1;
  for (int i = 1; i <= 40; ++i) List[i] = List[i - 1] * 2;
  F[0][0] = 1;
  for (int i = 1; i <= 40; ++i) {
    F[i][0] = 1;
    for (int j = 1; j <= i; ++j) F[i][j] = F[i - 1][j - 1] + F[i - 1][j];
  }
  for (int i = 0; i <= 40; ++i) {
    if (List[i] == T)
      Ct = i, flag = true;
    else if (List[i] > T)
      break;
  }
}
int main() {
  cin >> N >> T;
  Prework();
  if (!flag)
    cout << 0 << endl;
  else
    Solve();
  return 0;
}

```