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 matome_num():
    global num
    ans = num[0][0]
    for i in range(len(num)-1):
        if num[i][1] == num[i+1][1]:
            ans += num[i+1][0]
        else:
            num = [(ans,num[0][1])] + num[i+1:]
            return

    num = [(ans,num[0][1])]


n,x = map(int,raw_input().split())
old_num = map(int,raw_input().split())
mysum = sum(old_num)
num = [(1,mysum-old_num[n-i]) for i in range(1,n+1)]
ans = num[0][1]
while len(num) != 1:
    matome_num()
    if num[0][0] % x == 0:
        num[0] = (num[0][0]/x,num[0][1] + 1) 
    else:
        ans = num[0][1]
        break

if len(num) == 1:
    ans = num[0][1]
    y = num[0][0]
    while y % x == 0:
        y /= x
        ans += 1

INF = 1000000007

print pow(x,min(ans,mysum),INF)



