A8799 | 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".

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.

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