Consider sequences {A_1,...,A_N} of length N consisting of integers between 1 and K (inclusive).
There are K^N such sequences. Find the sum of $\gcd(A_1, ..., A_N)$ over all of them.
Since this sum can be enormous, print the value modulo (10^9+7).
Here $\gcd(A_1, ..., A_N)$ denotes the greatest common divisor of A_1, ..., A_N.

-----Constraints-----
- $2 \leq N \leq 10^5$
- $1 \leq K \leq 10^5$
- All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N K

-----Output-----
Print the sum of $\gcd(A_1, ..., A_N)$ over all K^N sequences, modulo (10^9+7).

-----Sample Input-----
3 2

-----Sample Output-----
9

$\gcd(1,1,1)+\gcd(1,1,2)+\gcd(1,2,1)+\gcd(1,2,2)+\gcd(2,1,1)+\gcd(2,1,2)+\gcd(2,2,1)+\gcd(2,2,2)=1+1+1+1+1+1+1+2=9$
Thus, the answer is 9.

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