Problem Description

Calculate the value of

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

modulo 19940417.

Input Format

The input consists of a single line with two integers $n$ and $m$.

Output Format

Output the answer modulo 19940417.

Sample Input and Output

Sample Input #1

3 4

Sample Output #1

1

Sample Input #2

123456 654321

Sample Output #2

116430

Notes

Data Size and Constraints

• For $10\%$ of the data, $n, m \leq 10^3$.
• For $30\%$ of the data, $n, m \leq 10^6$.
• For another $30\%$ of the data, $n \leq 100$.
• For $100\%$ of the data, $1 \leq n, m \leq 10^9$.

见题面 Input 部分

见题面 Output 部分