A10589 | Expression Queries

A simplified arithmetic expression (SAE) is an arithmetic expression defined by the following grammar:

- <SAE> ::= <Number> | <SAE>+<SAE> | <SAE>\*<SAE> | (<SAE>)
- <Number> ::= <Digit> | <Digit><Number>
- <Digit> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9

In other words it's a correct arithmetic expression that is allowed to contain brackets, numbers (possibly with leading zeros), multiplications and additions. For example expressions "(0+01)", "0" and "1\*(0)" are simplified arithmetic expressions, but expressions "2-1", "+1" and "1+2)" are not.

Given a string $s_{1}s_{2}...s_{|s|}$ that represents a SAE; $s_{i}$ denotes the $i$ -th character of the string which can be either a digit ('0'-'9'), a plus sign ('+'), a multiplication sign ('\*'), an opening round bracket '(' or a closing round bracket ')'.

A part $s_{l}s_{l+1}...s_{r}$ of this string is called a sub-expression if and only if it is a SAE.

You task is to answer $m$ queries, each of which is a pair of integers $l_{i}$ , $r_{i}$ $(1<=l_{i}<=r_{i}<=|s|)$ . For each query determine whether the corresponding part of the given string is a sub-expression and in case it's a sub-expression calculate its value modulo $1000000007 (10^{9}+7)$ . The values should be calculated using standard operator priorities.

The first line of the input contains non-empty string $s$ $(1<=|s|<=4·10^{5})$ which represents a correct SAE. Each character of the string can be one of the following characters: '\*', '+', '(', ')' or a digit ('0'-'9'). The expression might contain extra-huge numbers.

The second line contains an integer $m$ $(1<=m<=4·10^{5})$ which is the number of queries. Each of the next $m$ lines contains two space-separated integers $l_{i}$ , $r_{i}$ $(1<=l_{i}<=r_{i}<=|s|)$ — the $i$ -th query.

The $i$ -th number of output should be the answer for the $i$ -th query. If the $i$ -th query corresponds to a valid sub-expression output the value of the sub-expression modulo $1000000007 (10^{9}+7)$ . Otherwise output -1 as an answer for the query. Print numbers on separate lines.