#include <bits/stdc++.h>
#pragma comment(linker, "/stack:100000000")
using namespace std;
char s[55];
long long dp[55][55][2];
int bits(int x) {
  int r = 0;
  while (x != 0) {
    x &= (x - 1);
    ++r;
  }
  return r;
}
long long go(int p, int got, bool f) {
  if (dp[p][got][f] != -1) {
    return dp[p][got][f];
  } else if (p == 50) {
    return dp[p][got][f] = (got == 0 ? 1 : 0);
  } else {
    long long &res = dp[p][got][f];
    res = 0;
    int up = (f ? 1 : s[p] - '0');
    for (int i = 0; i <= up; i++) {
      res += go(p + 1, got - i, (i < up ? 1 : f));
    }
    return res;
  }
}
int main() {
  memset(dp, -1, sizeof(dp));
  long long n, t;
  cin >> n >> t;
  ++n;
  for (int(i) = 0; (i) < (50); (i)++) {
    if (n & (1LL << i)) {
      s[49 - i] = '1';
    } else {
      s[49 - i] = '0';
    }
  }
  for (int(i) = 0; (i) < (50); (i)++) {
    if (t == (1LL << i)) {
      long long res = go(0, i + 1, 0);
      if (i == 0) --res;
      cout << res;
      return 0;
    }
  }
  puts("0");
  return 0;
}

### Prompt

Generate 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>
#pragma comment(linker, "/stack:100000000")
using namespace std;
char s[55];
long long dp[55][55][2];
int bits(int x) {
  int r = 0;
  while (x != 0) {
    x &= (x - 1);
    ++r;
  }
  return r;
}
long long go(int p, int got, bool f) {
  if (dp[p][got][f] != -1) {
    return dp[p][got][f];
  } else if (p == 50) {
    return dp[p][got][f] = (got == 0 ? 1 : 0);
  } else {
    long long &res = dp[p][got][f];
    res = 0;
    int up = (f ? 1 : s[p] - '0');
    for (int i = 0; i <= up; i++) {
      res += go(p + 1, got - i, (i < up ? 1 : f));
    }
    return res;
  }
}
int main() {
  memset(dp, -1, sizeof(dp));
  long long n, t;
  cin >> n >> t;
  ++n;
  for (int(i) = 0; (i) < (50); (i)++) {
    if (n & (1LL << i)) {
      s[49 - i] = '1';
    } else {
      s[49 - i] = '0';
    }
  }
  for (int(i) = 0; (i) < (50); (i)++) {
    if (t == (1LL << i)) {
      long long res = go(0, i + 1, 0);
      if (i == 0) --res;
      cout << res;
      return 0;
    }
  }
  puts("0");
  return 0;
}

```