359_C. Prime Number
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.
```python
import sys
import heapq
input = sys.stdin.readline
MOD = int(1e9+7)

n, x = list(map(int, input().split()))
a = list(map(int, input().split()))
s, h = sum(a), []
for i in a:
    heapq.heappush(h, s-i)
p, cnt = 0, 0
while h:
    z = heapq.heappop(h)
    if p == z:
        cnt += 1
        if cnt == x:
            heapq.heappush(h, p + 1)
            cnt = 0
    else:
        if cnt > 0:
            print(pow(x, min(p, s), MOD))
            exit()
        cnt = 1
        p = z
print(pow(x, min(p, s), MOD))

```