Non-negative Partial Sums: Regional 2011 soutwestern Europa

You are given a sequence of n numbers a₀,..., a_n-1. A cyclic shift by k positions ( 0kn - 1) results in the following sequence: a_k, a_k+1,..., a_n-1, a₀, a₁,..., a_k-1. How many of the n cyclic shifts satisfy the condition that the sum of the first i numbers is greater than or equal to zero for all i with 1in?

Input 

Each test case consists of two lines. The first contains the number n ( 1n10⁶), the number of integers in the sequence. The second contains n integers a₀,..., a_n-1 ( -1000a_i1000) representing the sequence of numbers. The input will finish with a line containing 0.

Output 

For each test case, print one line with the number of cyclic shifts of the given sequence which satisfy the condition stated above.

Sample Input 

3
2 2 1
3
-1 1 1
1
-1
0

Sample Output 

3
2
0

Andrew and Strings-Codechef

http://www.codechef.com/problems/AMSTRING

Andrew likes strings very much.
He has two strings A and B of N lower alphabet letters. We denote S[i, j] as the substring from i^th to j^th characters of string S.
Andrew is interested in the number of such fours of integers (L_A, R_A, L_B, R_B), where 1 ≤ L_A ≤ R_A ≤ N, 1 ≤ L_B ≤ R_B ≤ N, and R_A − L_A = R_B − L_B, such that the Hamming distance between substrings A[L_A, R_A] and B[L_B, R_B] is not greater than K. Here the Hamming distance between two strings of the same length is the number of unequal characters on the same positions of strings.
Help him and find this number.

Input

The first line of the input contains an integer T, denoting the number of test cases. The description of T test cases follows. The first line of each test case contains two space-separated integers N and K. The second line contains string A, and the third line contains string B.

Output

For each test case, output an integer, denoting the number of fours (L_A, R_A, L_B, R_B) satisfying the conditions described in the problem statements.

Constraints

• 1 ≤ T ≤ 10
• 1 ≤ N ≤ 1000
• 1 ≤ K ≤ N
• Both A and B are contain only N lower alphabet letters

Example

Input:
3
3 2
aba
abb
3 2
abc
def
1 1
a
a

Output:
14
13
1

Explanation

Example case 1: There are 14 fours as following:
(1, 1, 1, 1) : dist(A[1, 1], B[1, 1]) = dist(a, a) = 0 ≤ 2
(1, 1, 2, 2) : dist(A[1, 1], B[2, 2]) = dist(a, b) = 1 ≤ 2
(1, 1, 3, 3) : dist(A[1, 1], B[3, 3]) = dist(a, b) = 1 ≤ 2
(2, 2, 1, 1) : dist(A[2, 2], B[1, 1]) = dist(b, a) = 1 ≤ 2
(2, 2, 2, 2) : dist(A[2, 2], B[2, 2]) = dist(b, b) = 0 ≤ 2
(2, 2, 3, 3) : dist(A[2, 2], B[3, 3]) = dist(b, b) = 0 ≤ 2
(3, 3, 1, 1) : dist(A[3, 3], B[1, 1]) = dist(a, a) = 0 ≤ 2
(3, 3, 2, 2) : dist(A[3, 3], B[2, 2]) = dist(a, b) = 1 ≤ 2
(3, 3, 3, 3) : dist(A[3, 3], B[3, 3]) = dist(a, b) = 1 ≤ 2
(1, 2, 1, 2) : dist(A[1, 2], B[1, 2]) = dist(ab, ab) = 0 ≤ 2
(1, 2, 2, 3) : dist(A[1, 2], B[2, 3]) = dist(ab, bb) = 1 ≤ 2
(2, 3, 1, 2) : dist(A[2, 3], B[1, 2]) = dist(ba, ab) = 2 ≤ 2
(2, 3, 2, 3) : dist(A[2, 3], B[2, 3]) = dist(ba, bb) = 1 ≤ 2
(1, 3, 1, 3) : dist(A[1, 3], B[1, 3]) = dist(aba, abb) = 1 ≤ 2
Example case 2: The four (1, 3, 1, 3) no longer satisfies the conditions, because
(1, 3, 1, 3) : dist(A[1, 3], B[1, 3]) = dist(abc, def) = 3 > 2