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.
[samples]
考虑以下文法：
该文法使用以下规则描述十进制系统中的数字：
例如，_2(2-4+1)+2(2(17))_ 描述整数 _2341234117171717_。
给定一个符合该文法的表达式，请输出其描述的整数对 #cf_span[109 + 7] 取模的结果。
输入仅有一行，包含一个非空字符串，长度不超过 #cf_span[105]，且符合上述文法。特别地，这意味着在形如 _l-r_ 的项中，#cf_span[l ≤ r] 成立。
请输出一个整数——该表达式所描述的数对 #cf_span[109 + 7] 取模的结果。
## Input
输入仅有一行，包含一个非空字符串，长度不超过 #cf_span[105]，且符合上述文法。特别地，这意味着在形如 _l-r_ 的项中，#cf_span[l ≤ r] 成立。
## Output
请输出一个整数——该表达式所描述的数对 #cf_span[109 + 7] 取模的结果。
[samples]
**Definitions**
Let $ G $ be a grammar over alphabet $ \Sigma = \{0,1,\dots,9, +, -, (, )\} $, with recursive production rules:
- A *term* is a digit $ d \in \{0,1,\dots,9\} $, or a compound expression of the form $ l - r $ or $ n(E) $, where:
- $ l, r $ are terms with $ l \leq r $ (inclusive range),
- $ n \in \mathbb{Z}_{\geq 1} $ is a positive integer (multiplier),
- $ E $ is a term.
The semantics of a term $ T $ is a string $ s(T) \in \{0,1,\dots,9\}^* $, defined recursively:
- If $ T = d $, then $ s(T) = d $ (as a string).
- If $ T = l - r $, then $ s(T) = \bigcup_{k=l}^{r} s(k) $, i.e., concatenation of strings $ s(l), s(l+1), \dots, s(r) $.
- If $ T = n(E) $, then $ s(T) = s(E)^n $, i.e., $ s(E) $ repeated $ n $ times.
Let $ N(T) $ be the integer value of the decimal string $ s(T) $, interpreted in base 10.
**Constraints**
- Input is a single string $ T $ of length $ \leq 10^5 $, valid under grammar $ G $.
- All numeric literals in ranges $ l, r $ satisfy $ l \leq r $.
**Objective**
Compute $ N(T) \mod (10^9 + 7) $.