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Longest Common Prefix II

Defining substring
For a string P with characters P1, P2 ,…, Pq, let us denote by P[i, j] the substring Pi, Pi+1 ,…, Pj.

Defining longest common prefix
LCP(S1, S2 ,…, SK), is defined as largest possible integer j such that S1[1, j] = S2[1, j] = … = SK[1, j].

You are given an array of N strings, A1, A2 ,…, AN and an integer K. Count how many indices (i, j) exist such that 1 ≤ i ≤ j ≤ N and LCP(Ai, Ai+1 ,…, Aj) ≥ K. Print required answer modulo 109+7.

Note that K does not exceed the length of any of the N strings. K <= min(len(A_i)) for all i

For example,

A = ["ab", "ac", "bc"] and K=1.

LCP(A[1, 1]) = LCP(A[2, 2]) = LCP(A[3, 3]) = 2
LCP(A[1, 2]) = LCP("ab", "ac") = 1
LCP(A[1, 3]) = LCP("ab", "ac", "bc") = 0
LCP(A[2, 3]) = LCP("ac", "bc") = 0

So, answer is 4.

Return your answer % MOD = 1000000007

1 ≤ Sum of length of all strings ≤ 5*105
Strings consist of small alphabets only.

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a doubt? Checkout Sample Codes for more details.
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