Yuanfang is puzzled with the question below:
There are n integers, a
1, a
2, …, a
n. The initial values of them are 0. There are four kinds of operations.
Operation 1: Add c to each number between a
x and a
y inclusive. In other words, do transformation a
k<---a
k+c, k = x,x+1,…,y.
Operation 2: Multiply c to each number between a
x and a
y inclusive. In other words, do transformation a
k<---a
k×c, k = x,x+1,…,y.
Operation 3: Change the numbers between a
x and a
y to c, inclusive. In other words, do transformation a
k<---c, k = x,x+1,…,y.
Operation 4: Get the sum of p power among the numbers between a
x and a
y inclusive. In other words, get the result of a
xp+a
x+1p+…+a
yp.
Yuanfang has no idea of how to do it. So he wants to ask you to help him.
Input
There are no more than 10 test cases.
For each case, the first line contains two numbers n and m, meaning that there are n integers and m operations. 1 <= n, m <= 100,000.
Each the following m lines contains an operation. Operation 1 to 3 is in this format: "1 x y c" or "2 x y c" or "3 x y c". Operation 4 is in this format: "4 x y p". (1 <= x <= y <= n, 1 <= c <= 10,000, 1 <= p <= 3)
The input ends with 0 0.
Output
For each operation 4, output a single integer in one line representing the result. The answer may be quite large. You just need to calculate the remainder of the answer when divided by 10007.