No Attacking

AtCoder

IDarc171_a

Time2000ms

Memory256MB

Difficulty—

There is a chessboard with $N$ rows and $N$ columns. Let $(i, j)$ denote the square at the $i$\-th row from the top and the $j$\-th column from the left. You will now place pieces on the board. There are two types of pieces, called **rooks** and **pawns**. A placement of pieces is called a **good arrangement** when it satisfies the following conditions: * Each square has zero or one piece placed on it. * If there is a rook at $(i, j)$, there is no piece at $(i, k)$ for all $k$ $(1 \leq k \leq N)$ where $k \neq j$. * If there is a rook at $(i, j)$, there is no piece at $(k, j)$ for all $k$ $(1 \leq k \leq N)$ where $k \neq i$. * If there is a pawn at $(i, j)$ and $i \geq 2$, there is no piece at $(i-1, j)$. Is it possible to place all $A$ rooks and $B$ pawns on the board in a good arrangement? You are given $T$ test cases; solve each of them. ## Constraints * $1 \leq T \leq 10^5$ * $1 \leq N \leq 10^4$ * $0 \leq A, B$ * $1 \leq A + B \leq N^2$ * All input values are integers. ## Input The input is given from Standard Input in the following format. Here, $\mathrm{case}_i$ represents the $i$\-th case. $T$ $\mathrm{case}_1$ $\mathrm{case}_2$ $\vdots$ $\mathrm{case}_T$ Each test case is given in the following format. $N$ $A$ $B$ [samples]

Samples

Input #1

8
5 2 3
6 5 8
3 2 2
11 67 40
26 22 16
95 91 31
80 46 56
998 2 44353

Output #1

Yes
No
No
No
Yes
No
Yes
Yes

In the first test case, for example, you can place rooks at $(1, 1)$ and $(2, 4)$, and pawns at $(3, 3)$, $(4, 2)$, and $(5, 3)$ to have all the pieces in a good arrangement.  
In the second test case, it is impossible to place all the pieces in a good arrangement.

API Response (JSON)

{
  "problem": {
    "name": "No Attacking",
    "description": {
      "content": "There is a chessboard with $N$ rows and $N$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and the $j$\\-th column from the left.   You will now place pieces on the board. Ther",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc171_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a chessboard with $N$ rows and $N$ columns. Let $(i, j)$ denote the square at the $i$\\-th row from the top and the $j$\\-th column from the left.  \nYou will now place pieces on the board. Ther...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments