Given a permutation a consisting of integers from 1 to n.
For a pair of indices i<j, with c=max(ai+1,ai+2,…,aj−1), the value of this pair is defined as:
- x if c≤min(ai,aj) or i=j−1.
- y if ai<c<aj or ai>c>aj.
- 0 in all other cases.
Given q queries l,r, calculate the total value of all pairs (a,b) such that l≤a<b≤r.
### Input
- The first line contains four integers n,q,x,y.
- The second line contains n integers representing the permutation a.
- The next q lines each contain two integers l,r representing a query.
### Output
- For each query, print the total value of all pairs that satisfy the condition.
### Constraints
- 1≤n,q≤2×105.
- 1≤x,y≤1000.
### Example
Input:
10523935410768121715195913
Output:
272038186
### Subtasks
- Subtask 1 (30% of the points): 1≤n,q≤500.
- Subtask 2 (30% of the points): x=2×y.
- Subtask 3 (40% of the points): No additional constraints.