#include <bits/stdc++.h>
using namespace std;
long long n, t;
map<pair<int, long long>, long long> mem;
long long res;
long long f(int id, long long t) {
  if (id == 1) return t == 1ll || t == 2ll;
  pair<int, long long> p = make_pair(id, t);
  if (mem.find(p) == mem.end()) {
    long long res = f(id - 1, t);
    if (t % 2ll == 0ll) res += f(id - 1, t / 2ll);
    mem[p] = res;
  }
  return mem[p];
}
long long g(int id, long long lin, long long t) {
  if (id == 1)
    return lin == 0 && t == 1ll || lin == 1 && (t == 1ll || t == 2ll);
  if (lin < 1ll << id - 1)
    return g(id - 1, lin, t);
  else {
    long long res = f(id - 1, t);
    if (t % 2ll == 0ll) res += g(id - 1, lin - (1ll << id - 1), t / 2ll);
    return res;
  }
}
int main() {
  scanf("%I64d %I64d", &n, &t);
  int id = 1;
  while (1ll << id + 1 <= n + 1ll) {
    res += f(id, t);
    id++;
  }
  res += g(id, n + 1ll - (1ll << id), t);
  printf("%I64d\n", res);
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
map<pair<int, long long>, long long> mem;
long long res;
long long f(int id, long long t) {
  if (id == 1) return t == 1ll || t == 2ll;
  pair<int, long long> p = make_pair(id, t);
  if (mem.find(p) == mem.end()) {
    long long res = f(id - 1, t);
    if (t % 2ll == 0ll) res += f(id - 1, t / 2ll);
    mem[p] = res;
  }
  return mem[p];
}
long long g(int id, long long lin, long long t) {
  if (id == 1)
    return lin == 0 && t == 1ll || lin == 1 && (t == 1ll || t == 2ll);
  if (lin < 1ll << id - 1)
    return g(id - 1, lin, t);
  else {
    long long res = f(id - 1, t);
    if (t % 2ll == 0ll) res += g(id - 1, lin - (1ll << id - 1), t / 2ll);
    return res;
  }
}
int main() {
  scanf("%I64d %I64d", &n, &t);
  int id = 1;
  while (1ll << id + 1 <= n + 1ll) {
    res += f(id, t);
    id++;
  }
  res += g(id, n + 1ll - (1ll << id), t);
  printf("%I64d\n", res);
  return 0;
}

```