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 <image> on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: <image>, 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

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

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

Examples

Input

2 2
2 2


Output

8


Input

3 3
1 2 3


Output

27


Input

2 2
29 29


Output

73741817


Input

4 5
0 0 0 0


Output

1

Note

In the first sample <image>. Thus, the answer to the problem is 8.

In the second sample, <image>. 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 <image>. Thus, the answer to the problem is 1.
def fast_mod(a, k, m):
    res = 1
    while (k > 0):
        if ((k & 1) == 1): res = res * a % m
        a = a * a % m
        k >>= 1
    return res

mod = 10 ** 9 + 7
n, m = map(int, raw_input().split())
a = map(int, raw_input().split())

res = fast_mod(m, sum(a) - a[n - 1], mod)
num = 0
cnt = n - 1
cnt_p = a[n - 1]

while True:
    cur_t = cnt
    while cnt >= 0:
        if a[cnt] == a[cur_t]:
            num += 1
        else:
            break
        cnt -= 1

    cur_k = cnt_p if cnt < 0 else min(cnt_p, a[cnt + 1] - a[cnt])
    while num % m == 0 and cur_k > 0:
        num /= m
        cur_k -= 1
        cnt_p -= 1
        res = res * m % mod
        
    if cur_k != 0 or cnt < 0:
        break
        
print res