F - Moving On

Description

Firdaws and Fatinah are living in a country with n

cities, numbered from 1 to n

. Each city has a risk of kidnapping or robbery.

Firdaws's home locates in the city u

, and Fatinah's home locates in the city v. Now you are asked to find the shortest path from the city u to the city v that does not pass through any other city with the risk of kidnapping or robbery higher than w

, a threshold given by Firdaws.

Input

The input contains several test cases, and the first line is a positive integer T

indicating the number of test cases which is up to 50

.

For each test case, the first line contains two integers n (1≤n≤200)

which is the number of cities, and q (1≤q≤2×104) which is the number of queries that will be given. The second line contains n integers r1,r2,⋯,rn indicating the risk of kidnapping or robbery in the city 1 to n respectively. Each of the following n lines contains n integers, the j-th one in the i-th line of which, denoted by di,j, is the distance from the city i to the city j

.

Each of the following q

lines gives an independent query with three integers u,v and w

, which are described as above.

We guarantee that 1≤ri≤105

, 1≤di,j≤105 (i≠j), di,i=0 and di,j=dj,i. Besides, each query satisfies 1≤u,v≤n and 1≤w≤105

.

Output

For each test case, output a line containing Case #x: at first, where x is the test case number starting from 1

. Each of the following q

lines contains an integer indicating the length of the shortest path of the corresponding query.

Sample Input

Input

1
3 6
1 2 3
0 1 3
1 0 1
3 1 0
1 1 1
1 2 1
1 3 1
1 1 2
1 2 2
1 3 2

Output

Case #1:
0
1
3
0
1
2

题意：求x到y的最短路，要求最短路上经过的城市危险度不能大于他给出的k

思路：flody，可以这么看，每两个点先判断能不能与危险度最低的城市连，连完后，然后再判断能不能与第次不危险的城市连。。。依次类推，这就是最外层k循环的含义

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