CF359C.Prime Number

普及/提高-

通过率：0%

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题目描述

Simon has a prime number $x$ and an array of non-negative integers $a_{1},a_{2},...,a_{n}$ .

Simon loves fractions very much. Today he wrote out number on a piece of paper. After Simon led all fractions to a common denominator and summed them up, he got a fraction: , where number $t$ equals $x^{a_{1}+a_{2}+...+a_{n}}$ . 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 $1000000007$ ( $10^{9}+7$ ).

输入格式

The first line contains two positive integers $n$ and $x$ ( $1<=n<=10^{5}$ , $2<=x<=10^{9}$ ) — the size of the array and the prime number.

The second line contains $n$ space-separated integers $a_{1},a_{2},...,a_{n}$ ( $0<=a_{1}<=a_{2}<=...<=a_{n}<=10^{9}$ ).

输出格式

Print a single number — the answer to the problem modulo $1000000007$ ( $10^{9}+7$ ).

输入输出样例

输入#1
```
2 2
2 2
```
输出#1
```
8
```
输入#2
```
3 3
1 2 3
```
输出#2
```
27
```
输入#3
```
2 2
29 29
```
输出#3
```
73741817
```
输入#4
```
4 5
0 0 0 0
```
输出#4
```
1
```

说明/提示

In the first sample . Thus, the answer to the problem is $8$ .

In the second sample, . 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 . Thus, the answer to the problem is $1$ .

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