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Range Shopping

Problem Description

Hamid is visiting a fair near his village. There are N shops of toys arranged in a line from left to right numbered 1 to N. There are two types of toys in each shop. The toy of type 1 costs A[i][0] coins and the toy of type 2 costs A[i][1] coins.

Now, he asks you to solve Q queries for him. Each query will be of type-

l r x y - He visits each shop from l to r in this order and he will buy exactly one toy from each of the visited shops. But, he wants to buy at least x toys of type 1 and at least y toys of type 2. Help him find the minimum cost for buying the toys. Since the answer can be large, return it modulo 109 + 7.



Problem Constraints

1 <= N, Q <= 105

1 <= l <= r <= N

0 <= x + y <= r-l+1

1 <= A[i][0], A[i][1] <= 109



Input Format

The first argument contains a 2D array A of size N x 2, denoting the prices of toys.

The second argument contains a 2D array B of size Q x 4, denoting the queires.



Output Format

Return an array of size Q denoting the answers to the queries. 



Example Input

Input 1:

  A : 
  [
    [1, 2]
    [4, 2]
    [3, 2]
    [4, 3]
  ]
  B : 
  [
    [2, 3, 1, 1]
    [1, 4, 2, 1]
  ]
Input 2:

  A : 
  [
    [2, 3]
    [4, 5]
    [2, 1]
  ]
  B : 
  [
    [2, 3, 0, 1]
  ]


Example Output

Output 1:

  [5, 9]
Output 2:

  [5]


Example Explanation

Explanation 1:

  1. You can buy toy of type 2 in shop 2 with cost 2 and toy of type 1 in shop 3 with cost 3. 
  2. You can buy toy of type 1 in shop 1 with cost 1, toy of type 2 in shop 2 with cost 3, 
     toy of type 1 in shop 3 with cost 3 and toy of type 2 in shop 4 with cost 3. 
     So, you bought 2 toys of type 1 and 2 toys of type 2.
Explanation 2:

  Buy toy of type 1 in shop 2 and toy of type 2 in shop 3.


NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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