Students of one unknown college don't have PE courses. That's why q of them decided to visit a gym nearby by themselves. The gym is open for n days and has a ticket system. At the i-th day, the cost of one ticket is equal to a_i. You are free to buy more than one ticket per day.

You can activate a ticket purchased at day i either at day i or any day later. Each activated ticket is valid only for k days. In other words, if you activate ticket at day t, it will be valid only at days t, t + 1, ..., t + k - 1. 

You know that the j-th student wants to visit the gym at each day from l_j to r_j inclusive. Each student will use the following strategy of visiting the gym at any day i (l_j ≤ i ≤ r_j):

  1. person comes to a desk selling tickets placed near the entrance and buy several tickets with cost a_i apiece (possibly, zero tickets); 
  2. if the person has at least one activated and still valid ticket, they just go in. Otherwise, they activate one of tickets purchased today or earlier and go in. 



Note that each student will visit gym only starting l_j, so each student has to buy at least one ticket at day l_j.

Help students to calculate the minimum amount of money they have to spend in order to go to the gym.

Input

The first line contains three integers n, q and k (1 ≤ n, q ≤ 300 000; 1 ≤ k ≤ n) — the number of days, the number of students and the number of days each ticket is still valid. 

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 10^9) — the cost of one ticket at the corresponding day.

Each of the next q lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n) — the segment of days the corresponding student want to visit the gym.

Output

For each student, print the minimum possible amount of money they have to spend in order to go to the gym at desired days.

Example

Input


7 5 2
2 15 6 3 7 5 6
1 2
3 7
5 5
7 7
3 5


Output


2
12
7
6
9

Note

Let's see how each student have to spend their money: 

  * The first student should buy one ticket at day 1. 
  * The second student should buy one ticket at day 3 and two tickets at day 4. Note that student can keep purchased tickets for the next days. 
  * The third student should buy one ticket at day 5. 
  * The fourth student should buy one ticket at day 7. 
  * The fifth student should buy one ticket at day 3 and one at day 4.

Source: codeforces | Difficulty: VERY_HARD
Tags: Dynamic programming

Data structures

Greedy algorithms


Solutions: