Today, more and more people begin to raise a QQpet. You can get a lot of pleasure from it, although it does not have a real life and it calls for huge patience to take care of it. There is a place called QQpet exploratory park in the world. Every week, you can get a chance to have a joy there for free. The whole park contains 61 grids in a line, numbered from 0 to 60. Ten of them are important grids which will touch off ( 引发 ) an incident when the pet stands on. They are 5, 12, 22, 29, 33, 38, 42, 46, 50 and 55. Your pet is standing on the gird of number 0 in the beginning. You can toss the die ( 掷骰子 ) 10 times. Each time, the pet goes ahead n steps which n is the number from the die ( n ∈{ 1, 2, …, 6 } ). If your RP is great enough( calls RPG for short ), you will get many surprises in the important grids, such as some yuanbao( the money in QQpet world ), an improvement of your pet's ability, and the most attractive gift-package. Now, your task is to calculate the probability(概率) of touching each important grid.

InputThe first line of the input contains an integer t–
determining the number of datasets. Then t lines follows. Each line
contains 6 numbers pi, i ∈{ 1, 2, …, 6 }, indicating the probability of
getting 1 to 6 after you toss the die every time . p1+ p2+ … + p6 = 1.

OutputFor each test case, output the probability of touching each
important grid. accurate up to 1 decimal places. There is a blank line
between test cases. See the Sample Output to get the exactly output
format.

Sample Input

2

0.000 1.000 0.000 0.000 0.000 0.000

0.500 0.000 0.000 0.000 0.000 0.500

Sample Output

5: 0.0%

12: 100.0%

22: 0.0%

29: 0.0%

33: 0.0%

38: 0.0%

42: 0.0%

46: 0.0%

50: 0.0%

55: 0.0%

5: 3.1%

12: 30.5%

22: 27.3%

29: 24.6%

33: 21.9%

38: 10.9%

42: 0.8%

46: 0.0%

50: 4.4%

55: 1.0%

OJ-ID： 
HDU-1493

author：
Caution_X

date of submission：
20190930

tags：
概率DP

description modelling：
投掷10次骰子，掷出的点数概率已给出，问掷完后落在5, 12, 22, 29, 33, 38, 42, 46, 50 55点上的概率。

major steps to solve it：
1.dp[i][j]:=第j次投在第i格上的概率，p[]:=各个点的概率
2.dp[i][1]=p[i];
3.dp[i+k][j+1]+=dp[i][j]*p[k];

AC CODE: