3058: Prime Number
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
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 
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 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).
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).
Print a single number − the answer to the problem modulo 1000000007 (109+7).
2 2
2 2
8
3 3
1 2 3
27
2 2
29 29
73741817
4 5
0 0 0 0
1
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 1073741824mod1000000007=73741817.
In the fourth sample 
. Thus, the answer to the problem is 1.