Wust_LL  is a math dalao(Chinglish). One day, he define a function: f(i,j), the value of which equals to the sum of all prime numbers which can divide LCM(i,j). LCM(i,j) means the Lowest Common Multiple of integer i and integer j.

Now Wust_LL  gets a Matrix with n rows and m columns. The value 

of Matrix[i][j]=f(i,j). He wants to know the sum of the Matrix[i][j](1≤i≤n,1≤j≤m). 

Each test case contains only one line with two integers n,m(1≤n,m≤10^6)

For each case, output an answer modulo 10^9+7.

2 2
4 2

6
18

we assume  is not a prime.