Maxim and Matrix

题意翻译

Maxim 喜欢以一种特殊的方式填写矩阵。这是一个填充大小矩阵的伪代码：  Maxim 会让您数有多少个 $m$（$1$ $\le$ $m$ $\le$ $n$），使得生成矩阵的行号 $m + 1$ 中的单元格中的值之和等于 $t$ 。

题目描述

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".

输入输出格式

输入格式

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.

输出格式

In a single line print a single integer — the answer to the problem.

输入输出样例

输入样例 #1

1 1

输出样例 #1

1

输入样例 #2

3 2

输出样例 #2

1

输入样例 #3

3 3

输出样例 #3

0

输入样例 #4

1000000000000 1048576

输出样例 #4

118606527258