Ntarsis has received two integers n and k for his birthday He wonders how many fibonacci-like sequences of length k can be formed with n as the k-th element of the sequenceA sequence of non-decreasing

To solve this problem, we can use dynamic programming to count the number of fibonacci-like sequences of length k.

First, we initialize an array dp of size k+1 with all elements set to 0. dp[i] will represent the number of fibonacci-like sequences of length i that end with the number n.

Next, we set dp[1] = 1 and dp[2] = 1, since there is only one fibonacci-like sequence of length 1 and 2 that ends with n.

Then, for i = 3 to k, we calculate dp[i] as the sum of dp[i-1] and dp[i-2]. This is because in order to form a fibonacci-like sequence of length i, we can either append n to a fibonacci-like sequence of length i-1 or append n to a fibonacci-like sequence of length i-2.

Finally, we output dp[k] as the answer for each test case.

Here is the implementation in Python:

t = int(input())

for _ in range(t): n, k = map(int, input().split())

dp = [0] * (k + 1) dp[1] = 1 dp[2] = 1

for i in range(3, k + 1): dp[i] = dp[i - 1] + dp[i - 2]

print(dp[k]