P7979 "Stoi2033" The World Has Not Ended Yet (Enhanced Version).

Note: **Using submission feedback to obtain testdata is cheating.** > Even if the world is about to collapse > My dear, I will never shed a tear > I will not give up that feeling of having loved > Cherishing everything that remembers you > Even if the world is about to tilt > My dear, I will never say goodbye > Even if the doomsday threat is stronger than ever > With love, it is not tiring > —— "The World Has Not Ended Yet"

Vinsta and Stella have $n$ piles of stones, and the $i$-th pile has $s_i$ stones. They agree to take turns starting from Vinsta. In each move, one may choose at least $1$ pile and at most $k$ piles. For the $i$-th pile, one may choose two real numbers $a, b$ such that: - $a \times b = s_i$ - $a + b = c, c \in [1, s_i] \cap \Z$ Then discard $c$ stones from the $i$-th pile, i.e., $s_i \leftarrow s_i - c$. The player who cannot make a move loses. They want to know whether Vinsta has a winning strategy.

The first line contains a positive integer $T$, the number of test cases. Then follow $T$ test cases. For each test case, the first line contains three positive integers $n, k, S$, where $S = \max\{s_i\}$. The second line contains $n$ positive integers $s_i$, representing the initial number of stones in the $i$-th pile.

For each test case, output one line. If there is a winning strategy, output `YES`, otherwise output `NO`.

For $100\%$ of the testdata, $1 \le T \le 10$, $1 \le k \le n \le 3 \times 10^6$, $1 \le S \le 3 \times 10^{17}$. Translated by ChatGPT 5