Today, Mr. Fox is taking it easy by playing with some blocks in a 2D world. Each block is an inch-by-inch square, and there are N stacks of blocks in a row, with the ith stack having H_i blocks. For example, if N=6 and H={3, 1, 5, 4, 1, 6}, then the collection of blocks looks like this (where an "X" denotes a block):

.....X
..X..X
..XX.X
X.XX.X
X.XX.X
XXXXXX

Ever curious, Mr. Fox would like to answer Q questions about his blocks (without actually modifying them), the ith one being as follows:

"If I were to consider only the stacks from A_i to B_i inclusive, getting rid of all of the other blocks, how many square inches of water would my block structure be able to hold?"

As one might imagine, a given square inch can hold water if it doesn't contain a block itself, but there is a block both somewhere to its left and somewhere to its right at the same height. For example, if you were to take A_i=2 and B_i=6, you would be left with the following block structure to consider (where an "*" denotes an inch-by-inch square which can hold water):

....X
.X**X
.XX*X
.XX*X
.XX*X
XXXXX

Constraints

1 ≤ T ≤ 20
1 ≤ N ≤ 300,000
1 ≤ Q ≤ 300,000
1 ≤ H_i ≤ 10⁹
1 ≤ A_i ≤ B_i ≤ N

Input

Input begins with an integer T, the number of block structures Mr. Fox has. For each structure, there is first a line containing the space-separated integers N and Q. The next line contains the space-separated integers H_i. Then follow Q lines, the ith of which contains the space-separated integers A_i and B_i.

Output

For the ith structure, print a line containing "Case #i: " followed by the sum of the answers to the Q questions modulo 10⁹+7.

Explanation of Sample

In the first case, we consider prefixes of the block structure. The answers to the queries are 0, 0, 0, 0, 0, 5, 5, 7, 7, 18, 18 for a total of 60.