#include <bits/stdc++.h>
using namespace std;
const long long int INF = 100010;
const long double eps = 0.000000001;
map<pair<long long int, int>, long long int> mem;
long long int g(long long int n, int pot) {
  if (mem.find(make_pair(n, pot)) != mem.end()) return mem[make_pair(n, pot)];
  if (n == 0) return 0;
  if (pot == 0) {
    int res = 0;
    while (n > 0) {
      n /= 2;
      res++;
    }
    return res;
  }
  long long int aux = 1;
  long long int m = n;
  while (m > 1) {
    m /= 2;
    aux *= 2;
  }
  long long int res = g(aux - 1, pot) + g(n - aux, pot - 1);
  mem[make_pair(n, pot)] = res;
  return res;
}
int main() {
  long long int n, t;
  cin >> n >> t;
  n++;
  int pot = 0;
  bool flag = true;
  while (t > 1) {
    if (t % 2 == 1) flag = false;
    t /= 2;
    pot++;
  }
  if (flag) {
    if (pot == 0)
      cout << g(n, pot) - 1 << endl;
    else
      cout << g(n, pot) << endl;
  } else {
    cout << 0 << endl;
  }
}

### Prompt

In Cpp, your task is to solve 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 long long int INF = 100010;
const long double eps = 0.000000001;
map<pair<long long int, int>, long long int> mem;
long long int g(long long int n, int pot) {
  if (mem.find(make_pair(n, pot)) != mem.end()) return mem[make_pair(n, pot)];
  if (n == 0) return 0;
  if (pot == 0) {
    int res = 0;
    while (n > 0) {
      n /= 2;
      res++;
    }
    return res;
  }
  long long int aux = 1;
  long long int m = n;
  while (m > 1) {
    m /= 2;
    aux *= 2;
  }
  long long int res = g(aux - 1, pot) + g(n - aux, pot - 1);
  mem[make_pair(n, pot)] = res;
  return res;
}
int main() {
  long long int n, t;
  cin >> n >> t;
  n++;
  int pot = 0;
  bool flag = true;
  while (t > 1) {
    if (t % 2 == 1) flag = false;
    t /= 2;
    pot++;
  }
  if (flag) {
    if (pot == 0)
      cout << g(n, pot) - 1 << endl;
    else
      cout << g(n, pot) << endl;
  } else {
    cout << 0 << endl;
  }
}

```