H. Function Composition
dfs and similar
We are definitely not going to bother you with another generic story when Alice finds about an array or when Alice and Bob play some stupid game. This time you'll get a simple, plain text.First, let us define several things. We define function \(F\) on the array \(A\) such that \(F(i, 1) = A[i]\) and \(F(i, m) = A[F(i, m - 1)]\) for \(m > 1\). In other words, value \(F(i, m)\) represents composition \(A[...A[i]]\) applied \(m\) times.You are given an array of length \(N\) with non-negative integers. You are expected to give an answer on \(Q\) queries. Each query consists of two numbers – \(m\) and \(y\). For each query determine how many \(x\) exist such that \(F(x,m) = y\).
The first line contains one integer \(N\) \((1 \leq N \leq 2 \cdot 10^5)\) – the size of the array \(A\). The next line contains \(N\) non-negative integers – the array \(A\) itself \((1 \leq A_i \leq N)\). The next line contains one integer \(Q\) \((1 \leq Q \leq 10^5)\) – the number of queries. Each of the next \(Q\) lines contain two integers \(m\) and \(y\) \((1 \leq m \leq 10^{18}, 1\leq y \leq N)\).
Output exactly \(Q\) lines with a single integer in each that represent the solution. Output the solutions in the order the queries were asked in.
For the first query we can notice that \(F(3, 10) = 1,\ F(9, 10) = 1\) and \(F(10, 10) = 1\).For the second query no \(x\) satisfies condition \(F(x, 5) = 7\).For the third query \(F(5, 10) = 6\) holds.For the fourth query \(F(3, 1) = 1.\)For the fifth query no \(x\) satisfies condition \(F(x, 10) = 8\).