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 calc(n,k,a):
    sTot=sum(a)
    biggest=max(a)
    m=10**9+7
    ans=pow(k,sTot-biggest,m)
    dic={}
    for i,item in enumerate(a):
        if biggest-item not in dic:
            dic[biggest-item]=1    
        else:
            dic[biggest-item]+=1
    # print(dic)
    extraPow=0
    i=0
    while dic[i]%k==0:
        if i+1 in dic:
            dic[i+1]+=dic[i]//k
        else:
            dic[i+1]=dic[i]//k
        i+=1
    val=pow(k,min(i,biggest),m)
    return (val*ans)%m

# print(pow(639134989,684686200,10**9+7))
# print(extractPow(98304,2))
n,k=list(map(int,input().split()))
a=list(map(int,input().split()))
print(calc(n,k,a))