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 $A_1, ..., A_N$.

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 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 $(10^9+7)$.