#include <bits/stdc++.h>
using namespace std;
long long t, n;
long long s[40][40];
long long temp[40];
long long degs[40];
void Precompute() {
  s[0][0] = 1;
  for (int i = 1; i <= 39; i++) {
    temp[0] = s[i - 1][0];
    for (int j = 1; j <= 39; j++) temp[j] = s[i - 1][j] + s[i - 1][j - 1];
    for (int j = 0; j <= 39; j++) s[i][j] = temp[j];
  }
  degs[0] = 1;
  for (int i = 1; i <= 39; i++) degs[i] = degs[i - 1] * 2;
}
long long ret;
long long degGet(long long t) {
  for (int i = 0; i <= 39; i++)
    if (degs[i] == t) return i;
  return -1;
}
int main() {
  Precompute();
  cin >> n >> t;
  long long deg = degGet(t);
  if (deg == -1) {
    cout << 0;
    return 0;
  }
  long long it = 1;
  while (n >= degs[it]) {
    ret += s[it][deg];
    n -= degs[it];
    it++;
  }
  int mul = 0;
  while (n > 0) {
    it = 39;
    while (degs[it] > n) it--;
    if (deg - mul < 0) break;
    ret += s[it][deg - mul];
    mul++;
    n -= degs[it];
  }
  cout << ret;
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 t, n;
long long s[40][40];
long long temp[40];
long long degs[40];
void Precompute() {
  s[0][0] = 1;
  for (int i = 1; i <= 39; i++) {
    temp[0] = s[i - 1][0];
    for (int j = 1; j <= 39; j++) temp[j] = s[i - 1][j] + s[i - 1][j - 1];
    for (int j = 0; j <= 39; j++) s[i][j] = temp[j];
  }
  degs[0] = 1;
  for (int i = 1; i <= 39; i++) degs[i] = degs[i - 1] * 2;
}
long long ret;
long long degGet(long long t) {
  for (int i = 0; i <= 39; i++)
    if (degs[i] == t) return i;
  return -1;
}
int main() {
  Precompute();
  cin >> n >> t;
  long long deg = degGet(t);
  if (deg == -1) {
    cout << 0;
    return 0;
  }
  long long it = 1;
  while (n >= degs[it]) {
    ret += s[it][deg];
    n -= degs[it];
    it++;
  }
  int mul = 0;
  while (n > 0) {
    it = 39;
    while (degs[it] > n) it--;
    if (deg - mul < 0) break;
    ret += s[it][deg - mul];
    mul++;
    n -= degs[it];
  }
  cout << ret;
  return 0;
}

```