Fibonacci Sum

Given two positive integers $k$ and $x$, determine whether $x$ can be written as the sum of exactly $k$ terms of the Fibonacci sequence. A term may be chosen more than once.

The Fibonacci sequence is defined by $F\_1 = F\_2 = 1$ and $F\_n = F\_{n-1} + F\_{n-2}$ for $n \geq 3$.

The first line contains the number of test cases $T$. $(1 \leq T \leq 100)$

Each of the next $T$ lines contains $k$, the number of Fibonacci terms to use, and $x$, the target positive integer, separated by a space. $(1 \leq k \leq 3;\, 1 \leq x \leq 10^{16})$

Print $T$ lines. On line $i$, print the answer for the $i$-th test case: YES if $x$ can be made by adding exactly $k$ Fibonacci terms, and NO otherwise.

The output is case-sensitive. Yes, yes, and similar forms are not accepted.

The input can exceed the range of an int. Using long long or another 64-bit type is recommended.

The output is case-sensitive. Yes and yes are not accepted as correct answers.