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E. More Queries to Array...

time limit per test

5 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou've got an array, consisting of *n* integers: *a*_{1}, *a*_{2}, ..., *a*_{n}. Your task is to quickly run the queries of two types:

- Assign value
*x*to all elements from*l*to*r*inclusive. After such query the values of the elements of array*a*_{l},*a*_{l + 1}, ...,*a*_{r}become equal to*x*. - Calculate and print sum , where
*k*doesn't exceed 5. As the value of the sum can be rather large, you should print it modulo 1000000007 (10^{9}+ 7).

Input

The first line contains two integers *n* and *m* (1 ≤ *n*, *m* ≤ 10^{5}), showing, how many numbers are in the array and the number of queries, correspondingly. The second line contains *n* integers: *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} ≤ 10^{9}) — the initial values of the array elements.

Then *m* queries follow, one per line:

- The assign query has the following format: "", (1 ≤
*l*≤*r*≤*n*; 0 ≤*x*≤ 10^{9}). - The query to calculate the sum has the following format: "", (1 ≤
*l*≤*r*≤*n*; 0 ≤*k*≤ 5).

All numbers in the input are integers.

Output

For each query to calculate the sum print an integer — the required sum modulo 1000000007 (10^{9} + 7).

Examples

Input

4 5

5 10 2 1

? 1 2 1

= 2 2 0

? 2 4 3

= 1 4 1

? 1 4 5

Output

25

43

1300

Input

3 1

1000000000 1000000000 1000000000

? 1 3 0

Output

999999986

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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