Prime Number

1000ms

262144K

Description:

Simon has a prime number x and an array of non-negative integers a₁, a₂, ..., a_n.

Simon loves fractions very much. Today he wrote out number $\text{[math]}$ on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: $\text{[math]}$ , where number t equals x^{a₁ + a₂ + ... + 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).

Input:

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, ..., a_n (0 ≤ a₁ ≤ a₂ ≤ ... ≤ a_n ≤ 10⁹).

Output:

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

Sample Input:

2 2
2 2

Sample Output:

Sample Input:

3 3
1 2 3

Sample Output:

Sample Input:

2 2
29 29

Sample Output:

73741817

Sample Input:

4 5
0 0 0 0

Sample Output:

Note:

In the first sample $\text{[math]}$ . Thus, the answer to the problem is 8.

In the second sample, $\text{[math]}$ . 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 $\text{[math]}$ . Thus, the answer to the problem is 1.

Informação

Provedor Codeforces

Código CF359C