#P756F. Long number

    ID: 3749 Type: RemoteJudge 2000ms 512MiB Tried: 0 Accepted: 0 Difficulty: (None) Uploaded By: Tags>expression parsingmathnumber theory*3400

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