Problem Statement

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.

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).

Constraints

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

Sample Input 1

3 2

Sample Output 1

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.

Sample Input 2

3 200

Sample Output 2

10813692

Sample Input 3

100000 100000

Sample Output 3

742202979

Be sure to print the sum modulo (10^9+7).

见题面 Input 部分

见题面 Output 部分