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 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 $10^{9} + 7$.

Input

The only line contains a non-empty string at most $10^{5}$ 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 $10^{9} + 7$.