Problem G
Teningakast

Dice by EsaRiutta, Pixabay

What dice to roll is given as a string. $n$d$m$ means one should roll $n$ $m$-sided dice and sum the results. Here $m$ sided dice are equally likely to give the results $1,2,\dots$ and up to $m$. $n$ and $m$ can be any strictly positive integers, but in this problem they will be less than ${10}^4$. $n$d$m!$ denotes exploding dice which means that if the highest possible result is rolled on the dice, i.e. $m$, then the dice should be rolled again and the results added together. This can happen over and over as long as the result continues to be equal to $m$. Exploding dice will never have $m=1$. The dice string is a sequence of dice rolls and numbers with $+$ or $-$ in between, possibly with a $-$ at the front. The numbers will also be less than ${10}^4$. For example 3d6+1d4!-2 means you should roll three six-sided dice, one exploding four sided die, add the results together and then subtract 2 from that total.

Input

The first line contains one integer $q$ ($1\le q\le {10}^5$). Then there are $q$ queries, each spanning $2$ lines. The first line contains a dice string as described above. The second line contains one integer $r$ ($-{10}^{18}\le r\le {10}^{18}$). The total length of all dice strings will be at most ${10}^5$ characters.

Output

Print Raunhaeft if the dice roll could result in $r$, print Svindl otherwise. Print the answers in the same order as the queries and print each reply on its own line.

Scoring

5
1d12+3
15
1d4+2d6
2
-1d6+1d4
-1
1d3!
100
1d6!-1d4!
0

Raunhaeft
Svindl
Raunhaeft
Raunhaeft
Raunhaeft