You'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 (109 + 7).

输入描述:

The first line contains two integers n and m (1 ≤ n, m ≤ 105), showing, how many numbers are in the array and the number of queries, correspondingly. The second line contains n integers: a1, a2, ..., an (0 ≤ ai ≤ 109) — 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 ≤ 109). The query to calculate the sum has the following format: "", (1 ≤ l ≤ r ≤ n; 0 ≤ k ≤ 5).All numbers in the input are integers.

输出描述:

For each query to calculate the sum print an integer — the required sum modulo 1000000007 (109 + 7).