Let $d(x)$ be the number of divisors of $x$. Given $N$ and $M$, calculate the value of $\sum_{i=1}^{N} \sum_{j=1}^{M} d(ij)$.
Input
The input contains multiple test cases. The first line contains an integer $T$, representing the number of test cases. The following $T$ lines each contain two integers $N$ and $M$.
Output
Output $T$ lines, each containing one integer representing the answer.
Examples
Input 1
2 7 4 5 6
Output 1
110 121
Constraints
| Test Case ID | Range of $N, M$ | Range of $T$ |
|---|---|---|
| 1 | $1 \le N, M \le 100$ | $1 \le T \le 50000$ |
| 2 | ||
| 3 | $1 \le N, M \le 1000$ | $1 \le T \le 10$ |
| 4 | ||
| 5 | ||
| 6 | $1 \le N, M \le 50000$ | $1 \le T \le 50000$ |
| 7 | ||
| 8 | ||
| 9 | ||
| 10 |