Another Contest 3 Problem 4 - Range Updates and Range Queries

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Points: 15
Time limit: 2.0s
Memory limit: 256M

Problem types

You have an array of N integers, initialized all to zero to begin with. Support two operations.

INCREMENT l r a - For each index i between l and r, increase the ith element of the array by a \cdot (i-l+1).

SUM l r - Compute the sum of the integers between indices l and r, inclusive.


1 \le N \le 10^6

1 \le Q \le 10^5

1 \le l_i \le r_i \le N

1 \le a_i \le 5

Input Specification

The first line contains two positive integers, N and Q.

The next Q lines each contain a sequence of positive integers. If the first integer in the line is 1, then three integers follow, l_i, r_i, and a_i, indicating an INCREMENT operation.

Otherwise, the first integer in the line is 2, and then two integers follow, l_i and r_i, indicating a SUM operation.

Output Specification

For each SUM operation, output on its own line the result of the query. The data will be set such that this fits in a signed 32-bit integer.

Sample Input

3 4
1 2 3 2
2 1 1
2 2 2
2 3 3

Sample Output



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