A dice string
Practice
3.7 (3 votes)
Dynamic programming
Matrix
Probability spaces
Algorithms
Probablity
Modular exponentiation
Problem
12% Success 322 Attempts 30 Points 1s Time Limit 256MB Memory 1024 KB Max Code

You are given a dice having six faces numbered as 1, 2, 3, 4, 5, and 6 respectively. You throw the dice \(n\) times and the outcomes are written serially in order to form an n-digit number. You are required to find the probability that the number formed is divisible by 11.

Input format

  • The first line consists of a single integer \(T\) denoting the number of test cases
  • Each of the next \(T\) lines contains a single integer \(n\) denoting the number of throws

Output format

The output must consist of \(T\) lines where each contains a single integer representing the required probability.

Print the answer modulo \(10^9+7\). If the answer is of the form \(\frac PQ\), then print \(PQ^{-1} (mod\ 10^9+7)\).

Constraints

\(1\le T\le 100\\1\le n \le 10^{18}\)

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