#include <bits/stdc++.h>
using namespace std;
long long N, T;
int L;
long long DP[64][64][2];
int inp[64];
long long rec(int pos, int remOne, int flag) {
  if (pos == L) {
    if (remOne == 0)
      return 1LL;
    else
      return 0LL;
  }
  if (DP[pos][remOne][flag] != -1) return DP[pos][remOne][flag];
  long long ans = 0;
  int newFlag = flag;
  if (inp[pos] == 1) newFlag = 1;
  ans += rec(pos + 1, remOne, newFlag);
  if (remOne >= 1) {
    if (inp[pos] == 1 || flag) ans += rec(pos + 1, remOne - 1, flag);
  }
  return DP[pos][remOne][flag] = ans;
}
int main() {
  cin >> N >> T;
  long long temp = T;
  int power = 0;
  while (temp > 1) {
    if (temp % 2 != 0) {
      cout << 0 << endl;
      return 0;
    }
    power++;
    temp /= 2;
  }
  power++;
  memset(DP, -1, sizeof(DP));
  temp = N + 1;
  L = 0;
  while (temp > 0) {
    inp[L++] = temp % 2;
    temp /= 2;
  }
  reverse(inp, inp + L);
  long long ans = rec(0, power, 0);
  if (power == 1) ans--;
  cout << ans << endl;
  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>
using namespace std;
long long N, T;
int L;
long long DP[64][64][2];
int inp[64];
long long rec(int pos, int remOne, int flag) {
  if (pos == L) {
    if (remOne == 0)
      return 1LL;
    else
      return 0LL;
  }
  if (DP[pos][remOne][flag] != -1) return DP[pos][remOne][flag];
  long long ans = 0;
  int newFlag = flag;
  if (inp[pos] == 1) newFlag = 1;
  ans += rec(pos + 1, remOne, newFlag);
  if (remOne >= 1) {
    if (inp[pos] == 1 || flag) ans += rec(pos + 1, remOne - 1, flag);
  }
  return DP[pos][remOne][flag] = ans;
}
int main() {
  cin >> N >> T;
  long long temp = T;
  int power = 0;
  while (temp > 1) {
    if (temp % 2 != 0) {
      cout << 0 << endl;
      return 0;
    }
    power++;
    temp /= 2;
  }
  power++;
  memset(DP, -1, sizeof(DP));
  temp = N + 1;
  L = 0;
  while (temp > 0) {
    inp[L++] = temp % 2;
    temp /= 2;
  }
  reverse(inp, inp + L);
  long long ans = rec(0, power, 0);
  if (power == 1) ans--;
  cout << ans << endl;
  return 0;
}

```