C. Banh-mitime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputJATC 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.InputThe first line contains two integers n and q (1 \le n, q \le 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 \le l_i \le r_i \le n) — the segment of the corresponding query.OutputPrint q lines, where i-th of them contains a single integer — the answer to the i-th query modulo 10^9 + 7.ExamplesInput4 210111 43 4Output143Input3 21111 23 3Output31NoteIn 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.
Input4 210111 43 4
Output143
['greedy', 'implementation', 'math', '*1600']