N integers are arranged on a circle clockwise. Given two integers M and K. For each position, you should take M continuous integers on the left and M continuous integers on the right. Take out the K-th number of the 2M integers. Then you will get N integers. Add all the integers up and tell me the sum. If the answer is not smaller than 1,000,000,007, divide it by 1,000,000,007 and tell me the remainder.
Input
There is an Integer T in the first line. Which means the number of test cases in the input file. Then followed by T test cases.
For each test case, in the first line there are 3 Integers N(5<=N<=100,000),M(0<M*2<N),K(0<K<2*M). Then there are N Integers, all the integers are non-negative Integers and smaller than 1,000,000,000.