Description:
Simon has a prime number x and an array of non-negative integers a1, a2, ..., an.
Simon loves fractions very much. Today he wrote out number $$\frac{1}{x^{a_1}} + \frac{1}{x^{a_2}} + \ldots + \frac{1}{x^{a_n}}$$ on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: $$\text{S}$$, where number t equals xa1 + a2 + ... + an. 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).
Input Format:
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).
Output Format:
Print a single number — the answer to the problem modulo 1000000007 (109 + 7).
Note:
In the first sample $$\frac{1}{4} + \frac{1}{4} = \frac{4+4}{16} = \frac{8}{16}$$. Thus, the answer to the problem is 8.
In the second sample, $$\frac{1}{3}+\frac{1}{9}+\frac{1}{27}=\frac{243+81+27}{729}=\frac{351}{729}$$. 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 $$\frac{1}{1}+\frac{1}{1}+\frac{1}{1}+\frac{1}{1}=\frac{4}{1}$$. Thus, the answer to the problem is 1.