Problem Statement

Tanaka, a high school student, is taking a math test.
However, there is a problem he cannot solve, and at this rate he will get a failing grade.
That problem is to solve a single-variable polynomial containing derivatives.

Tanaka's brain is connected to the Internet, so even during the test he can send an expression to a computer and receive the answer.
For Tanaka's sake, write a program that calculates and solves the given expression.

The only operators appearing in the expression are '+', representing addition, and '*', representing multiplication.
The values appearing in the expression are constants, the variable 'x', and the derivative "d{$f(x)$}" of an expression $f(x)$.
(The derivative of $f(x)$ is $\frac{d}{dx}\{f(x)\}$ in the usual Leibniz notation, but it is written as "d{$f(x)$}" to simplify the expression.)

Note that because the operators are limited, the n-th power of $x$ is represented as a multiplication of n copies of $x$, as in $x^n=x*x*x*...*x*x$.
The operator precedence is '+' < '*', the same as in the real world.

Input

$N$
$d$
$S$

$N$ represents the number of characters in the string $S$ representing the expression.
$d$ represents the maximum degree of the variable x appearing in the expression (before differentiation).
$S$ is a string of length $N$ representing the expression. $S$ contains no spaces.

$1 \le N=|S| \le 50000$
$0 \le d \le 10$

The expression $S$ contains the operators '+' and '*', constants, the variable 'x', and derivatives "d{$T$}". $T$ is also a string representing an expression, and $1\le|T|$ is guaranteed.
Also, each constant appearing in the expression is an integer between 1 and 9, inclusive.

No single term contains two or more constants.
That is, there is no input containing a term in which constants appear two or more times, such as "2*2*x".
The constant is not necessarily at the beginning of a term, as in "x*2".

The only operator that can be adjacent to a derivative is '+'.
That is, there is no input such as "x*d{x}"

Output

$A_{0} \: A_{1} \: A_{2} \: ... \: A_{d-1} \: A_{d}$

Find the result $A_{0}*x^{0}+A_{1}*x^{1}+...+A_{d}*x^{d}$ of calculating all the derivatives contained in the expression.
Output the coefficients $A_{0},A_{1},A_{2},... ,A_{d-1},A_{d}$ of $x_{0},x_{1},x_{2},... ,x_{d-1},x_{d}$.
Be careful about the values of the coefficients in the result.
Print a newline at the end.

Sample

8
2
d{x*x+x}

1 2 0

19
3
d{2*x+d{3*x*x*x}}+x

2 19 0 0

1
1
x

0 1

59
3
x*x*x+d{x*x*x}+d{d{x*x*x}}+d{d{d{x*x*x}}}+d{d{d{d{x*x*x}}}}

6 6 3 1