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):

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

inputFormat

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.

outputFormat

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

样例

1000000000000 1048576

118606527258