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Problem Statement

Dr. Suposupo developed a programming language called Shipura. Shipura supports only one binary operator ${\\tt >>}$ and only one unary function ${\\tt S<\\ >}$.

$x {\\tt >>} y$ is evaluated to $\\lfloor x / 2^y \\rfloor$ (that is, the greatest integer not exceeding $x / 2^y$), and ${\\tt S<} x {\\tt >}$ is evaluated to $x^2 \\bmod 1{,}000{,}000{,}007$ (that is, the remainder when $x^2$ is divided by $1{,}000{,}000{,}007$).

The operator ${\\tt >>}$ is left-associative. For example, the expression $x {\\tt >>} y {\\tt >>} z$ is interpreted as $(x {\\tt >>} y) {\\tt >>} z$, not as $x {\\tt >>} (y {\\tt >>} z)$. Note that these parentheses do not appear in actual Shipura expressions.

The syntax of Shipura is given (in BNF; Backus-Naur Form) as follows:

expr   ::= term | expr sp ">>" sp term
term   ::= number | "S" sp "<" sp expr sp ">"
sp     ::= "" | sp " "
number ::= digit | number digit
digit  ::= "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"```

The start symbol of this syntax is $\\tt expr$ that represents an expression in Shipura. In addition, $\\tt number$ is an integer between $0$ and $1{,}000{,}000{,}000$ inclusive, written without extra leading zeros.

Write a program to evaluate Shipura expressions.

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### Input

The input is a sequence of datasets. Each dataset is represented by a line which contains a valid expression in Shipura.

A line containing a single ${\\tt \\#}$ indicates the end of the input. You can assume the number of datasets is at most $100$ and the total size of the input file does not exceed $2{,}000{,}000$ bytes.

### Output

For each dataset, output a line containing the evaluated value of the expression.

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### Sample Input

```plain
S< S< 12 >> 2 > >
123 >> 1 >> 1
1000000000   >>129
S<S<S<S<S<2>>>>>
S  <S< S<2013    >>> 11 >>> 10 >
#```

### Output for the Sample Input

```plain
81
30
0
294967268
14592400```

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### Source Name

[JAG Practice Contest for ACM-ICPC Asia Regional 2013](http://acm-icpc.aitea.net/index.php?2013%2FPractice%2F%CC%CF%B5%BC%C3%CF%B6%E8%CD%BD%C1%AA)

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