Double Remainder Product Sum

Given two positive integers n and m, compute the sum:

$$ S = \sum_{i=1}^{n} \sum_{j=1}^{m} (n \bmod i) \times (m \bmod j) \quad \text{for } i \neq j, $$

and output the result modulo 19940417.

Note: The summation is taken over all pairs \((i, j)\) with \(1 \le i \le n\) and \(1 \le j \le m\) such that \(i \neq j\).

inputFormat

The input consists of two integers n and m separated by spaces or newlines.

outputFormat

Output a single integer representing the computed value of \(S \bmod 19940417\).

sample

2 2

0