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{"ops":[{"attributes":{"bold":true},"insert":"Is this prime?"},{"insert":"\nProblem Statement\nLet's assume some functional definitions for this problem.\nWe take prime(x) as the set of all prime divisors of x. For example, prime(140)={2,5,7}, prime(169)={13}.\n\nLet f(x,p) be the maximum possible integer p**k where k is an integer such that x is divisible by p**k.\n(Here a**b means a raised to the power b or pow(a, b))\nFor example:\nf(99,3)=9 (99 is divisible by 3**2=9 but not divisible by 3**3=27),\nf(63,7)=7 (63 is divisible by 7**1=7 but not divisible by 7**2=49).\n\nLet g(x,y) be the product of f(y,p) for all p in prime(x).\nFor example:\ng(30,70)=f(70,2)*f(70,3)*f(70,5)=2*1*5=10,\ng(525,63)=f(63,3)*f(63,5)*f(63,7)=9*1*7=63.\nYou are given two integers x and n. Calculate g(x,1)*g(x,2)*\u2026*g(x,n) mod (1000000007).\n(Read modulo exponentiation before attempting this problem)\nInput\nThe only line contains integers x and n \u2014 the numbers used in formula.\nConstraints\n2 \u2264 x \u2264 1000000000\n1 \u2264 n \u2264 1000000000000000000\nOutput\nPrint the answer corresponding to the input.\n\n"}]}

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