Problem: JATC loves Banh-mi (a Vietnamese food). His affection for Banh-mi is so much that he always has it for breakfast. This morning, as usual, he buys a Banh-mi and decides to enjoy it in a special way.

First, he splits the Banh-mi into n parts, places them on a row and numbers them from 1 through n. For each part i, he defines the deliciousness of the part as x_i ∈ \{0, 1\}. JATC's going to eat those parts one by one. At each step, he chooses arbitrary remaining part and eats it. Suppose that part is the i-th part then his enjoyment of the Banh-mi will increase by x_i and the deliciousness of all the remaining parts will also increase by x_i. The initial enjoyment of JATC is equal to 0.

For example, suppose the deliciousness of 3 parts are [0, 1, 0]. If JATC eats the second part then his enjoyment will become 1 and the deliciousness of remaining parts will become [1, \\_, 1]. Next, if he eats the first part then his enjoyment will become 2 and the remaining parts will become [\\_, \\_, 2]. After eating the last part, JATC's enjoyment will become 4.

However, JATC doesn't want to eat all the parts but to save some for later. He gives you q queries, each of them consisting of two integers l_i and r_i. For each query, you have to let him know what is the maximum enjoyment he can get if he eats all the parts with indices in the range [l_i, r_i] in some order.

All the queries are independent of each other. Since the answer to the query could be very large, print it modulo 10^9+7.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 100 000).

The second line contains a string of n characters, each character is either '0' or '1'. The i-th character defines the deliciousness of the i-th part.

Each of the following q lines contains two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ n) — the segment of the corresponding query.

Output

Print q lines, where i-th of them contains a single integer — the answer to the i-th query modulo 10^9 + 7.

Examples

Input

4 2
1011
1 4
3 4


Output

14
3


Input

3 2
111
1 2
3 3


Output

3
1

Note

In the first example: 

  * For query 1: One of the best ways for JATC to eats those parts is in this order: 1, 4, 3, 2. 
  * For query 2: Both 3, 4 and 4, 3 ordering give the same answer. 



In the second example, any order of eating parts leads to the same answer.

Solution (in PYTHON3):

Solution:
# Causes TLE
# C++17 implemention -> 1062c.cpp

MOD = 1000000007

def main():
    buf = input()
    buflist = buf.split()
    n = int(buflist[0])
    q = int(buflist[1])
    buf = input()
    x = buf
    sum_list = [0] # sentinel / one indexing
    for i, deliciousness in enumerate(x):
        sum_list.append(int(deliciousness) + sum_list[i])
    enjoyment_list = [0]
    for i in range(n):
        enjoyment_list.append((enjoyment_list[i] * 2 + 1) % MOD)
    query_list = []
    for i in range(q):
        buf = input()
        buflist = buf.split()
        l = int(buflist[0]) # one indexing
        r = int(buflist[1]) # one indexing
        query_list.append((l, r))
    for i, query in enumerate(query_list):
        l = query[0]
        r = query[1]
        banhmi_count = r - l + 1
        delicious_count = sum_list[r] - sum_list[l - 1]
        non_delicious_count = banhmi_count - delicious_count
        enjoyment = 0
        # main part
        if delicious_count == 0:
            enjoyment = 0
        else:
            enjoyment += enjoyment_list[delicious_count]
            enjoyment += (enjoyment_list[banhmi_count] - enjoyment_list[delicious_count] - enjoyment_list[non_delicious_count])
            enjoyment = enjoyment % MOD
        print(enjoyment)

if __name__ == '__main__':
    main()