More Queries to Array...

You've got an array, consisting of n integers: a1, a2, ..., an. Your task is to quickly run the queries of two types:

1. Assign value x to all elements from l to r inclusive. After such query the values of the elements of array al, al + 1, ..., ar become equal to x.
2. 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).

Input

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:

1. The assign query has the following format: "", (1 ≤ l ≤ r ≤ n; 0 ≤ x ≤ 109).
2. 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 (109 + 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

inputFormat

Input

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:

1. The assign query has the following format: "", (1 ≤ l ≤ r ≤ n; 0 ≤ x ≤ 109).
2. The query to calculate the sum has the following format: "", (1 ≤ l ≤ r ≤ n; 0 ≤ k ≤ 5).

All numbers in the input are integers.

outputFormat

Output

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

样例

4 5
5 10 2 1
? 1 2 1
= 2 2 0
? 2 4 3
= 1 4 1
? 1 4 5

                                                              25
                                                          43
                                                        1300

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