Calculate $\sum\limits_{i=1}^n \sum\limits_{j=1}^m [i \ne j] (n \bmod i) (m \bmod j)$.

Input

The first line contains two integers $n$ and $m$.

Output

Output a single integer representing the answer modulo $19\,940\,417$.

Examples

Input 1

3 4

Output 1

1

Note 1

The answer is $\begin{split}(3 \bmod 1)\times(4 \bmod 2)+(3 \bmod 1) \times (4 \bmod 3)+(3 \bmod 1) \times (4 \bmod 4) + (3 \bmod 2) \times (4 \bmod 1) + (3 \bmod 2) \times (4 \bmod 3) +\\ (3 \bmod 2) \times (4 \bmod 4) + (3 \bmod 3) \times (4 \bmod 1) + (3 \bmod 3) \times (4 \bmod 2) + (3 \bmod 3) \times (4 \bmod 4) = 1\end{split}$

Constraints

For $10\%$ of the data, $n, m \leq 1\,000$;

For $30\%$ of the data, $n, m \leq 1\,000\,000$;

Additionally, for $30\%$ of the data, $n \leq 100$ and $m \leq 10^9$;

For $100\%$ of the data, $n, m \leq 10^9$.