Summing XOR Pairs

Given two positive integers \(n\) and \(m\), compute the following sum:

\[ S = \sum_{i=1}^{n}\sum_{j=1}^{m}\left(i\oplus j\right) \mod 998244353, \]

where \(\oplus\) denotes the bitwise XOR operation (the same as the '^' operator in C++).

inputFormat

The input consists of a single line that contains two positive integers \(n\) and \(m\) separated by a space.

\(1 \leq n, m \leq 10^{9}\)

outputFormat

Output a single integer, the sum \(S\) modulo \(998244353\).

sample

1 1

0