262_E. Maxim and Matrix
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):

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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
```python
def comb(n, r):
    if r > n or r < 0:
        return 0
    r = min(r, n-r)
    result = 1
    for i in range(1, r+1):
        result = result*(n+1-i)//i
    return result

def F(n, t):
    if t == 0:
        return 1
    elif n == 0:
        return 0
    elif n == 1:
        return int(t == 1)
    m = len(bin(n)) - 3
    return F(n-(1 << m), t-1) + comb(m, t)

n, t = map(int, input().strip().split())
T = len(bin(t)) - 3
if (1 << T) != t:
    print(0)
else:
    print(F(n+1, T+1) - int(t == 1))

```