Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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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 2010-2017 Mike Mirzayanov

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