1941: Expression Queries
Description
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 s1s2...s|s| that represents a SAE; si 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 slsl+1...sr 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 li, ri (1≤li≤ri≤|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(109+7). The values should be calculated using standard operator priorities.
The first line of the input contains non-empty string s (1≤|s|≤4·105) 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≤4·105) which is the number of queries. Each of the next m lines contains two space-separated integers li, ri (1≤li≤ri≤|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(109+7). Otherwise output -1 as an answer for the query. Print numbers on separate lines.
((1+2)*3+101*2)
6
8 14
1 6
2 10
11 14
5 5
4 5
205
-1
10
2
2
-1
(01)
1
1 4
1