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C. Maxim and Matrix

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMaxim 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* ≤ 10^{12}, *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

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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