Long number

题面翻译

考虑下面的算法（设 A，B 为自然数）：

• A ：表示 A 本身。
• A-B ：不间断地输出 A 到 B 之间的数（ $A\le B$ ），例如 8-11，表示 891011。
• A(B)：把数字 B 重复 A 遍。
• A+B：连接数字 A 和 B。

举个例子，2(2-4+1)+2(2(17)) 表示的数是 2341234117171717。
现在请你输出在如上规则下的数对 $10^9+7$ 取余的结果（输入的长度不超过 $10^5$）。

题目描述

Consider the following grammar:

• ::= | '+'
• ::= | '-' | '(' ')'
• ::= <pos_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:

• describes itself,
• - (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,
• () describes integer which is concatenation of copies of integer described by ,
• + describes integer which is concatenation of integers described by and .

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 $10^{9}+7$ .

输入格式

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.

输出格式

Print single integer — the number described by the expression modulo $10^{9}+7$ .

样例 #1

样例输入 #1

8-11

样例输出 #1

891011

样例 #2

样例输入 #2

2(2-4+1)+2(2(17))

样例输出 #2

100783079

样例 #3

样例输入 #3

1234-5678

样例输出 #3

745428774

样例 #4

样例输入 #4

1+2+3+4-5+6+7-9

样例输出 #4

123456789