Solve the programming task below in a Python markdown code block.
A permutation of length N is an array of N integers (P_{1},P_{2}, \dots,P_{N}) where every integer from 1 to N (inclusive) appears in it exactly once. The weight of a subsegment containing the elements (P_{l},P_{l+1}, \dots,P_{r}) is defined as follows:  W(l, r) = (r-l+1)\cdot \min\limits_{l≤ i ≤ r} (P_{i})
where 1≤ l ≤ r ≤ N and \min\limits_{l≤ i ≤ r} (P_{i}) denotes the minimum element of the subsegment.

You are given two integers N and X. You need to determine if there exists a permutation of length N such that it contains at least one subsegment having weight X?

------ Input Format ------ 

- The first line contains an integer T - the number of test cases. The T test cases then follow.
- The first and only line of each test case contains two space-separated integers N, X - the length of the permutation and the weight parameter mentioned in the question respectively.

------ Output Format ------ 

For each test case, print YES if there exists a permutation of length N having at least one subsegment with a weight of X, otherwise print NO.

You may print each character of Yes and No in uppercase or lowercase (for example, yes, yEs, YES will be considered identical).

------ Constraints ------ 

$1 ≤ T ≤ 10^{4}$
$1 ≤ N ≤ 10^{5}$
$1 ≤ X ≤ 10^{10}$
- Sum of $N$ over all test cases does not exceed $3 \cdot 10^{5}$.

----- Sample Input 1 ------ 
4
3 2
3 5
5 6
4 10

----- Sample Output 1 ------ 
YES
NO
YES
NO

----- explanation 1 ------ 
Test case $1$: $[1, 2, 3]$ is one of the valid permutations because it contains the following subsegment having weight $2$. 

$W(1, 2) = (2-1+1) \cdot \min\limits_{1≤ i ≤ 2} (P_{i})= 2 \cdot 1=2$ 

Test case $2$: It can be proven that there does not exist any permutation of length $3$ which has a subsegment having weight $5$.

Test case $3$: $[4, 2, 1, 3, 5]$ is one of the valid permutations because it contains the following subsegment having weight $6$.

$W(4, 5)=(5-4+1) \cdot \min\limits_{4≤ i ≤ 5} (P_{i})= 2 \cdot 3=6$