#P756F. Long number
Long number
No submission language available for this problem.
Description
Consider the following grammar:
- <expression> ::= <term> | <expression> '+' <term>
- <term> ::= <number> | <number> '-' <number> | <number> '(' <expression> ')'
- <number> ::= <pos_digit> | <number> <digit>
- <digit> ::= '0' | <pos_digit>
- <pos_digit> ::= '1' | '2' | '3' | '4' | '5' | '6' | '7' | '8' | '9'
This grammar describes a number in decimal system using the following rules:
- <number> describes itself,
- <number>-<number> (l-r, l ≤ r) describes integer which is concatenation of all integers from l to r, written without leading zeros. For example, 8-11 describes 891011,
- <number>(<expression>) describes integer which is concatenation of <number> copies of integer described by <expression>,
- <expression>+<term> describes integer which is concatenation of integers described by <expression> and <term>.
For example, 2(2-4+1)+2(2(17)) describes the integer 2341234117171717.
You are given an expression in the given grammar. Print the integer described by it modulo 109 + 7.
The only line contains a non-empty string at most 105 characters long which is valid according to the given grammar. In particular, it means that in terms l-r l ≤ r holds.
Print single integer — the number described by the expression modulo 109 + 7.
Input
The only line contains a non-empty string at most 105 characters long which is valid according to the given grammar. In particular, it means that in terms l-r l ≤ r holds.
Output
Print single integer — the number described by the expression modulo 109 + 7.
Samples
8-11
891011
2(2-4+1)+2(2(17))
100783079
1234-5678
745428774
1+2+3+4-5+6+7-9
123456789