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: 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 . 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). 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 . 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.