Problem1617--Long number

1617: Long number

Time Limit: 2 Sec  Memory Limit: 256 MB
Submit: 0  Solved: 0
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Description

time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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.

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.

Examples
Input
8-11
Output
891011
Input
2(2-4+1)+2(2(17))
Output
100783079
Input
1234-5678
Output
745428774
Input
1+2+3+4-5+6+7-9
Output
123456789

Source/Category

 
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