AND and SUM

AtCoder

IDabc238_d

Time2000ms

Memory256MB

Difficulty—

Solve the following problem for $T$ test cases. > Given are non-negative integers $a$ and $s$. Is there a pair of non-negative integers $(x,y)$ that satisfies both of the conditions below? > > * $x\ \text{AND}\ y=a$ > * $x+y=s$ What is bitwise $\mathrm{AND}$?The bitwise $\mathrm{AND}$ of integers $A$ and $B$, $A\ \mathrm{AND}\ B$, is defined as follows: * When $A\ \mathrm{AND}\ B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if those of $A$ and $B$ are **both** $1$, and $0$ otherwise. For example, we have $4\ \mathrm{AND}\ 6 = 4$ (in base two: $100\ \mathrm{AND}\ 110 = 100$). ## Constraints * $1 \leq T \leq 10^5$ * $0 \leq a,s \lt 2^{60}$ * All values in input are integers. ## Input Input is given from Standard Input. The first line is in the following format: $T$ Then, $T$ test cases follow. Each test case is in the following format: $a$ $s$ [samples]

Samples

Input #1

2
1 8
4 2

Output #1

Yes
No

In the first test case, some pairs such as $(x,y)=(3,5)$ satisfy the conditions.
In the second test case, no pair of non-negative integers satisfies the conditions.

Input #2

4
201408139683277485 381410962404666524
360288799186493714 788806911317182736
18999951915747344 451273909320288229
962424162689761932 1097438793187620758

Output #2

No
Yes
Yes
No

API Response (JSON)

{
  "problem": {
    "name": "AND and SUM",
    "description": {
      "content": "Solve the following problem for $T$ test cases. > Given are non-negative integers $a$ and $s$. Is there a pair of non-negative integers $(x,y)$ that satisfies both of the conditions below? >  > *   $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc238_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Solve the following problem for $T$ test cases.\n\n> Given are non-negative integers $a$ and $s$. Is there a pair of non-negative integers $(x,y)$ that satisfies both of the conditions below?\n> \n> *   $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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