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

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

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