SON OF SUN

There is the Sun $a_0$ and $2N$ people $a_1,a_2,\ldots,a_{2N}$, numbered from $0$ through $2N$.

Choose one parent for every person to form a family tree rooted at the Sun. The Sun has no parent. The parent of $a_i$ must be some $a_j$ with a smaller index, so $0\leq j<i$ for every .

Let $w(i)$ denote the energy of $a_i$. The energies are

In index order, they are

The family of $a_i$ consists of $a_i$ and all descendants of $a_i$. Let be the sum of the energies of everyone in this family.

Given a positive integer $N$ and an integer $k$, determine whether the parent relationships can be chosen so that

A correct decision about whether $k$ lies between the minimum and maximum attainable sums for the given $N$ also earns $50\%$ of each subtask score. See the Output section for the scoring rules.

The input is given in the following format:

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

For each test case, print YES if a valid family tree exists, and NO otherwise.

The output is case-insensitive.

Scoring

Let $L_N,R_N$ be the minimum and maximum attainable sums for the given $N$. The interval decision is YES if , and otherwise. The output format remains one or for each case.

• $1\leq T\leq200\,000$.
• $1\leq N\leq200\,000$.
• $-{10}^{}$.