Sum of gcd of Tuples (Hard)

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).

Examples

Input

3 2

Output

9

Input

3 200

Output

10813692

Input

100000 100000

Output

742202979

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N K

outputFormat

Output

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

Examples

Input

3 2

Output

9

Input

3 200

Output

10813692

Input

100000 100000

Output

742202979

样例

100000 100000

742202979