Isaac is a passionate competitive programmer, especially fascinated by convolution techniques used in ICPC problems. During the lectures of last year's Training Camp Mexico (TCMX for short), he mastered bitwise convolutions:

• AND convolution: for each $$$k$$$, $$$$$$ C[k] = \sum_{i \,\&\, j = k} A[i] \cdot B[j] $$$$$$
• OR convolution: for each $$$k$$$, $$$$$$ C[k] = \sum_{i \,|\, j = k} A[i] \cdot B[j] $$$$$$
• XOR convolution: for each $$$k$$$, $$$$$$ C[k] = \sum_{i \,\oplus\, j = k} A[i] \cdot B[j] $$$$$$

He implemented all of them successfully with SOS DP and used them to solve problems involving fast subset transforms.

This year, during the Tercera Fecha del Gran Premio de México ICPC 2025, which coincides with the third contest of this year's TCMX, Isaac is facing a problem involving a new and intriguing type: MOD convolution. It is defined similarly to the bitwise convolutions, but replacing the bitwise index condition with a modular remainder condition:

$$$$$$ C[k] = \sum_{\substack{1 \leq i \leq n \\ k \lt j\leq m \\ i \equiv k\bmod{j}}} A[i] \cdot B[j] $$$$$$

As everyone knows, MOD convolution can be easily calculated using $$$\blacksquare\blacksquare\blacksquare$$$.

The problem asks, given arrays $$$A$$$ of length $$$n$$$ and $$$B$$$ of length $$$m$$$, to compute: $$$$$$ \sum_{k=0}^{\infty} k \cdot C[k]. $$$$$$

Where $$$C[k]$$$ is defined as in the MOD convolution above.

Just like Isaac, you are also competing in the Tercera Fecha del Gran Premio de México ICPC 2025, and you should find the answer for this problem.