Jumping sequence

AtCoder

IDabc221_g

Time5000ms

Memory256MB

Difficulty—

Consider an infinite two-dimensional coordinate plane. Takahashi, who is initially standing at $(0,0)$, will do $N$ jumps in one of the four directions he chooses every time: up, down, left, or right. The length of each jump is fixed. Specifically, the $i$\-th jump should cover the distance of $D_i$. Determine whether it is possible to be exactly at $(A, B)$ after $N$ jumps. If it is possible, show one way to do so. Here, for each direction, a jump of length $D$ from $(X, Y)$ takes him to the following point: * up: $(X,Y) \to (X,Y+D)$ * down: $(X,Y) \to (X,Y-D)$ * left: $(X,Y) \to (X-D,Y)$ * right: $(X,Y) \to (X+D,Y)$. ## Constraints * $1 \leq N \leq 2000$ * $\lvert A\rvert, \lvert B\rvert \leq 3.6\times 10^6$ * $1 \leq D_i \leq 1800$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A$ $B$ $D_1$ $D_2$ $\ldots$ $D_N$ [samples]

Samples

Input #1

3 2 -2
1 2 3

Output #1

Yes
LDR

If he jumps left, down, right in this order, Takahashi moves $(0,0)\to(-1,0)\to(-1,-2)\to(2,-2)$ and ends up at $(2, -2)$, which is desired.

Input #2

2 1 0
1 6

Output #2

No

It is impossible to be exactly at $(1, 0)$ after the two jumps.

Input #3

5 6 7
1 3 5 7 9

Output #3

Yes
LRLUR

API Response (JSON)

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  "problem": {
    "name": "Jumping sequence",
    "description": {
      "content": "Consider an infinite two-dimensional coordinate plane. Takahashi, who is initially standing at $(0,0)$, will do $N$ jumps in one of the four directions he chooses every time: up, down, left, or right.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 5000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc221_g"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Consider an infinite two-dimensional coordinate plane. Takahashi, who is initially standing at $(0,0)$, will do $N$ jumps in one of the four directions he chooses every time: up, down, left, or right....",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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