Simon has a prime number x and an array of non-negative integers a 1, a 2, ..., a n . Simon loves fractions very much. Today he wrote out number on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: , where number t equals x a 1 + a 2 + ... + a n . Now Simon wants to reduce the resulting fraction. Help him, find the greatest common divisor of numbers s and t . As GCD can be rather large, print it as a remainder after dividing it by number 1000000007 (109 + 7).

输入描述:

The first line contains two positive integers n and x (1 ≤ n ≤ 105, 2 ≤ x ≤ 109) — the size of the array and the prime number.The second line contains n space-separated integers a1, a2, ..., an (0 ≤ a1 ≤ a2 ≤ ... ≤ an ≤ 109).

输出描述:

Print a single number — the answer to the problem modulo 1000000007 (109 + 7).

备注:

In the first sample . Thus, the answer to the problem is 8.In the second sample, . The answer to the problem is 27, as 351 = 13·27, 729 = 27·27.In the third sample the answer to the problem is 1073741824 mod 1000000007 = 73741817.In the fourth sample . Thus, the answer to the problem is 1.