Problem3599--Maxim and Matrix

3599: Maxim and Matrix

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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