Primes and Multiplication

Let's introduce some definitions that will be needed later.

Let prime(x) be the set of prime divisors of x. For example, prime(140) = { 2, 5, 7 }, prime(169) = { 13 }.

Let g(x, p) be the maximum possible integer p^k where k is an integer such that x is divisible by p^k. For example:

• g(45, 3) = 9 (45 is divisible by 3^2=9 but not divisible by 3^3=27),
• g(63, 7) = 7 (63 is divisible by 7^1=7 but not divisible by 7^2=49).

Let f(x, y) be the product of g(y, p) for all p in prime(x). For example:

• f(30, 70) = g(70, 2) ⋅ g(70, 3) ⋅ g(70, 5) = 2^1 ⋅ 3^0 ⋅ 5^1 = 10,
• f(525, 63) = g(63, 3) ⋅ g(63, 5) ⋅ g(63, 7) = 3^2 ⋅ 5^0 ⋅ 7^1 = 63.

You have integers x and n. Calculate f(x, 1) ⋅ f(x, 2) ⋅ … ⋅ f(x, n) mod{(10^{9} + 7)}.

Input

The only line contains integers x and n (2 ≤ x ≤ 10^{9}, 1 ≤ n ≤ 10^{18}) — the numbers used in formula.

Output

Print the answer.

Examples

Input

10 2

Output

2

Input

20190929 1605

Output

363165664

Input

947 987654321987654321

Output

593574252

Note

In the first example, f(10, 1) = g(1, 2) ⋅ g(1, 5) = 1, f(10, 2) = g(2, 2) ⋅ g(2, 5) = 2.

In the second example, actual value of formula is approximately 1.597 ⋅ 10^{171}. Make sure you print the answer modulo (10^{9} + 7).

In the third example, be careful about overflow issue.

inputFormat

Input

The only line contains integers x and n (2 ≤ x ≤ 10^{9}, 1 ≤ n ≤ 10^{18}) — the numbers used in formula.

outputFormat

Output

Print the answer.

Examples

Input

10 2

Output

2

Input

20190929 1605

Output

363165664

Input

947 987654321987654321

Output

593574252

Note

In the first example, f(10, 1) = g(1, 2) ⋅ g(1, 5) = 1, f(10, 2) = g(2, 2) ⋅ g(2, 5) = 2.

In the second example, actual value of formula is approximately 1.597 ⋅ 10^{171}. Make sure you print the answer modulo (10^{9} + 7).

In the third example, be careful about overflow issue.

样例

20190929 1605

363165664

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