Let's call a sequence of integers a₁, a₂, ..., a_N almost monotonic if first K elements are non-decreasing sequence and last N-K+1 elements are non-increasing sequence: a₁≤a₂≤...≤a_K and a_K≥a_K+1≥...≥a_N.

The diversity number of a sequence a₁, a₂, ..., a_N is the number of possible sequences b₁, b₂,..., b_N for which 0≤b_i<a_i and all of the numbers b₁, b₂,..., b_N are different. The diversity number of an empty sequence is 1.

You need to find the sum of the diversity numbers of all almost monotonic subsequences of a sequence. Since this number can be very large, find it modulo 1,000,000,007. A subsequence is a sequence that can be obtained from another sequence by deleting some elements without changing the order of the remaining elements. Two sequences are considered different if their lengths differ or there is at least one position at which they differ.

Input

The first line of the input file consists of a single number T, the number of test cases. Each test case consists of a number M, the number of elements in a sequence, followed by M numbers n, elements of some sequence (note that this sequence is not necessarily almost monotonic). All tokens are whitespace-separated

Constraints

T = 20
1 ≤ M, n ≤ 100

Output

Output T lines, with the answer to each test case on a single line.