P7977 “Stoi2033” The World Has Not Yet Ended.

Note: **Using submission feedback to extract data is cheating**. > Even if the world is about to collapse > Darling, I will never shed a tear > I will not give up that feeling of having loved > Cherishing everything that holds memories of you > Even if the world is about to tilt > Darling, I will never say goodbye > Even if the doomsday threat is even stronger > With love, it is not tiring > —— “The World Has Not Yet Ended”

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

The first line contains three positive integers $n, k, S$, where $S = \max\{s_i\}$. The second line contains $n$ positive integers $s_i$, which represent the initial number of stones in the $i$-th pile.

Output one line. If there is a winning strategy, output `YES`; otherwise output `NO`.

### Constraints **This problem uses bundled testdata.** | Subtask | $1 \le n \le$ | $1 \le S \le$ | Score | | :-: | :-: | :-: | :-: | | $1$ | $300$ | $300$ | $7$ | | $2$ | $300$ | $3 \times 10^7$ | $8$ | | $3$ | $300$ | $3\times 10^{10}$ | $16$ | | $4$ | $3\times 10^6$ | $3$ | $3$ | | $5$ | $3\times 10^6$ | $3 \times 10^3$ | $3$ | | $6$ | $3\times 10^6$ | $3 \times 10^7$ | $16$ | | $7$ | $3\times 10^6$ | $3\times 10^{10}$ | $47$ | For $100\%$ of the data, $1 \le k \le n \le 3 \times 10^6$, and $1 \le S \le 3 \times 10^{10}$. Translated by ChatGPT 5