B. Lipshitz Sequence
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

A function is called Lipschitz continuous if there is a real constant K such that the inequality |f(x) - f(y)| ≤ K·|x - y| holds for all . We'll deal with a more... discrete version of this term.

For an array , we define it's Lipschitz constant as follows:

• if n < 2, • if n ≥ 2, over all 1 ≤ i < j ≤ n

In other words, is the smallest non-negative integer such that |h[i] - h[j]| ≤ L·|i - j| holds for all 1 ≤ i, j ≤ n.

You are given an array of size n and q queries of the form [l, r]. For each query, consider the subarray ; determine the sum of Lipschitz constants of all subarrays of .

Input

The first line of the input contains two space-separated integers n and q (2 ≤ n ≤ 100 000 and 1 ≤ q ≤ 100) — the number of elements in array and the number of queries respectively.

The second line contains n space-separated integers ( ).

The following q lines describe queries. The i-th of those lines contains two space-separated integers li and ri (1 ≤ li < ri ≤ n).

Output

Print the answers to all queries in the order in which they are given in the input. For the i-th query, print one line containing a single integer — the sum of Lipschitz constants of all subarrays of .

Examples
Input
10 41 5 2 9 1 3 4 2 1 72 43 87 101 9
Output
178223210
Input
7 65 7 7 4 6 6 21 22 32 61 74 73 5
Output
202259168
Note

In the first query of the first sample, the Lipschitz constants of subarrays of with length at least 2 are:

• • • The answer to the query is their sum.