p02715 AtCoder Beginner Contest 162 - 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
```python
mod = 10 ** 9 + 7

N, K = map(int, input().split())

A = [0] + [pow(K // x, N, mod) for x in range(1, K + 1)]
for x in reversed(range(1, K + 1)):
    for i in range(2, K // x + 1):
        A[x] -= A[i * x]

print(sum(i * a for i, a in enumerate(A)) % mod)
```