B"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 in {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 . 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$$"...