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.
from math import ceil,log
def exp(a,p,m):
    if(p==0):
        return 1
    elif(p==1):
        return a%m
    elif(p%2==0):
        x = exp(a,p/2,m)
        return (x*x)%m
    else:
        return (a*exp(a,p-1,m))%m
n,x = map(int,raw_input().split())
a = [int(i) for i in raw_input().split()]
s = sum(a)
A =[s-a[i] for i in xrange(n)]
A.sort(reverse=True)
cnt = 0
while(1):
    v = A[-1]
    cnt=0
    while(len(A)>0 and A[-1]==v):
        cnt+=1
        A.pop()
    if(cnt%x!=0):
        v = min(v,s)
        print exp(x,v,(10**9)+7)
        break
    else:
        cnt/=x
        for i in xrange(cnt):
            A.append(v+1)
    
