题目描述
Being in a long distance relationship, giving time to your girlfriend, focusing on your job and maintaining fitness, doing all three of these is not an easy task.
So, to save time, Pankaj has decided to multi task some things together. Now job and girlfriend are a very deadly mix, so he has decided to walk from his office to his house while talking/chatting with his girlfriend at the same time (he will look around for traffic and make sure he doesn't get hit by a car or a bus).
Now, there are certain landmarks in the city and there are roads connecting these landmarks where he can walk in either direction. Now, to avoid going through the same path every day (well it will become boring at some time), Pankaj has decided to compute how many distinct walks he can take from his office to his house. He knows it takes one unit of time to walk on any road between the landmarks and he knows that his girlfriend will be free for only a certains units of time (She has other things to do like studying, gossiping with other girls etc). So, instead of wasting any time, he would like to travel on only that many roads.
Given the map of the city where he lives, with n landmarks, his office location u (meaning his office is the u^th landmark), location of his house v (meaning his house is the v^th landmark) and k (the exact number of roads he would like to travel),
find the number of distinct walks from u to v in the city with exactly k number of roads on the walk. Since this number can be too long, find the result modulo 1000000007.
He will consider two walks are distinct if either they use different road or the sequence of roads on the walks is different.
Input
The first line of the input will consist of T, the number of test cases.
Each test case will be as follows:
First line of each test case contains four space separated integers n, k, u and v.
Then n lines follow, each line contains n space separated integers with value either 0 or 1. If the j^th integer in the i^th line is 1, it means there is a road connecting landmark i with landmark j, otherwise it the integer is 0, there is no connecting road between them.
Output:
T lines, each containing the required answer.
Constraints
0 < T ≤ 50
1 < n ≤ 50
0 ≤ k ≤ 10^18
0 ≤ u ≤ N-1
0 ≤ v ≤ N-1
SAMPLE INPUT
2
3 1 2 1
0 1 1
1 0 1
1 1 0
4 4 0 3
0 0 0 1
0 0 1 0
0 1 0 1
1 0 1 0
SAMPLE OUTPUT
1
0
输入格式
见题面
输出格式
见题面
样例输入
50
49 400000000001692800 5 29
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0 1 1 0 0 0 1 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 0 1 1 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 0 0 1 0
0 1 0 0 0 0 1 1 1 1 0 1 1 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 1 0 1
1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 1 1 1 0 1 0 0 1 0 0 0 0 1 1 1 0 0 0 1 1 0
1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 1 0
1 1 0 0 0 1 0 0 0 1 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 0
1 1 0 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 1 1 0 0 0 1 1 0 0 0 1 0 1 1 1 0 0 1 0 1 1 1 1 1 1 0 0
0 0 1 1 1 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 1
0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 1 1 0 1 1 0 0 1
1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 1 1
1 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 0 1 1 1 0 0
1 1 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 1 0 1 0 0 1 1 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 0 1 1 0 0 0 1
0 0 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 1 1 0 0 1 0
1 0 0 0 0 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0 1 1 1 1 1 0 0 0 0 0 1 1 0 1 0 1 0 1
1 1 1 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 0 0 0 1 1 1 1 1 0 1 1
1 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0 1
0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 0 1 1 1 0 1 0 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1
1 0 1 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 1 1 0 0 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 0 1 0
1 1 1 1 1 0 1 0 1 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 1 0 1 1 1 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 1
1 0 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 0
1 0 1 1 1 1 0 0 1 1 1 1 0 1 1 1 1 1 1 1 0 0 0 0 0 1 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 1
1 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 0 0 1 1 1 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 0 1 1 1 1 0 0 1 0
0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 0 0 1
0 1 1 1 0 1 1 1 0 0 1 0 1 0 1 1 1 1 1 1 1 1 1 0 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 0 1 1 0 0 0
1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 0 0
样例输出
304257890
68732065
941814225
467241299
324384835
524503528
191862828
57948508
435462367
141380399
166509620
515911607
720389156
649102673
852241937
717623780
27013463
505972478
445104468
855946040
512659120
426894642
612947883
207611136
375837393
567151039
968637346
127911201
194295302
431057768
386975249
624084604
983319030
800983637
583072827
997834306
866485618
896204818
635213412
461656360
376267155
150818535
752262418
575410719
384910277