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 qp(n, m):
    rt = 1
    while m:
        if m & 1:
            rt = rt * n % int(1e9+7)
        m >>= 1
        n = n * n % int(1e9+7)
    return rt
n, x = map(int, raw_input().split())
a = map(int, raw_input().split())
s = sum(a)
for i in xrange(n):
    a[i] = s - a[i]
a.sort()
cy = 1
nw = a[0]
f = 0
for i in xrange(1, n):
    if a[i] != nw:
        while nw != a[i]:
            if cy % x != 0:
                f = 1
                break
            cy /= x
            nw += 1
        if f:
            break
    cy += 1
while cy % x == 0:
    cy /= x
    nw += 1
nw = min(s, nw)
print qp(x, nw)
