Bobo wants to count the number of matrices $A$ that satisfy the following conditions:

1. Matrix $A$ has $n$ rows and $m$ columns, and every element is a positive integer. The element in the $i$-th row and $j$-th column is denoted by $A_{i, j}$.
2. $A_{1, 1} = 2018$.
3. For all $2 \leq i \leq n, 1 \leq j \leq m$, $A_{i, j}$ is a divisor of $A_{i - 1, j}$.
4. For all $1 \leq i \leq n, 2 \leq j \leq m$, $A_{i, j}$ is a divisor of $A_{i, j - 1}$.

Since the number of such matrices $A$ can be very large, Bobo only wants to find the number of such matrices modulo $(10^9+7)$.

Input

The input contains multiple test cases. Process until the end of the file.

Each test case contains two integers $n$ and $m$.

Output

For each test case, output one integer representing the number of such matrices modulo $(10^9+7)$.

Examples

Input 1

1 1
1 2
2 2
2 3
2000 2000

Output 1

1
4
25
81
570806941

Note

For the second test case ($n = 1, m = 2$), the matrices $A$ that satisfy the conditions are $(2018, 2018), (2018, 1009), (2018, 2), (2018, 1)$, totaling $4$ possibilities.

Constraints

• $1 \leq n, m \leq 2000$
• The number of test cases does not exceed $10^5$.