#include <bits/stdc++.h>
using namespace std;
const int INF = 2147483647;
const long long LLINF = 9223372036854775807LL;
const int maxn = 45;
long long comb[maxn][maxn];
int a[maxn];
int main() {
  long long t, n;
  cin >> n >> t;
  if (t & (t - 1)) printf("0\n"), exit(0);
  long long tt = t;
  int pp = 0;
  while (tt) ++pp, tt >>= 1;
  for (int i = 0; i < maxn; ++i) comb[i][0] = 1;
  for (int i = 1; i < maxn; ++i)
    for (int j = 1; j < maxn; ++j)
      comb[i][j] = comb[i - 1][j] + comb[i - 1][j - 1];
  int len = 0;
  ++n;
  while (n) {
    a[len++] = n & 1;
    n >>= 1;
  }
  reverse(a, a + len);
  int has = 0;
  long long ans = 0;
  for (int i = 0; i < len; ++i) {
    if (a[i]) {
      int rem = pp - has;
      if (rem >= 0) ans += comb[len - i - 1][rem];
    }
    has += a[i];
  }
  if (has == pp) ++ans;
  if (pp == 1) ans--;
  cout << ans << endl;
  return 0;
}

### Prompt

Your challenge is to write 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;
const int INF = 2147483647;
const long long LLINF = 9223372036854775807LL;
const int maxn = 45;
long long comb[maxn][maxn];
int a[maxn];
int main() {
  long long t, n;
  cin >> n >> t;
  if (t & (t - 1)) printf("0\n"), exit(0);
  long long tt = t;
  int pp = 0;
  while (tt) ++pp, tt >>= 1;
  for (int i = 0; i < maxn; ++i) comb[i][0] = 1;
  for (int i = 1; i < maxn; ++i)
    for (int j = 1; j < maxn; ++j)
      comb[i][j] = comb[i - 1][j] + comb[i - 1][j - 1];
  int len = 0;
  ++n;
  while (n) {
    a[len++] = n & 1;
    n >>= 1;
  }
  reverse(a, a + len);
  int has = 0;
  long long ans = 0;
  for (int i = 0; i < len; ++i) {
    if (a[i]) {
      int rem = pp - has;
      if (rem >= 0) ans += comb[len - i - 1][rem];
    }
    has += a[i];
  }
  if (has == pp) ++ans;
  if (pp == 1) ans--;
  cout << ans << endl;
  return 0;
}

```