D. Plus and xor

Codeforces

IDCF76D

Time2000ms

Memory256MB

Difficulty—

dpgreedymath

English · Original

Chinese · Translation

Formal · Original

Bitwise exclusive OR (or bitwise addition modulo two) is a binary operation which is equivalent to applying logical exclusive OR to every pair of bits located on the same positions in binary notation of operands. In other words, a binary digit of the result is equal to 1 if and only if bits on the respective positions in the operands are different. For example, if _X_ = 10910 = 11011012, _Y_ = 4110 = 1010012, then: <center>_X_ _xor_ _Y_ = 6810 = 10001002.</center>Write a program, which takes two non-negative integers _A_ and _B_ as an input and finds two non-negative integers _X_ and _Y_, which satisfy the following conditions: * _A_ = _X_ + _Y_ * _B_ = _X_ _xor_ _Y_, where _xor_ is bitwise exclusive or. * _X_ is the smallest number among all numbers for which the first two conditions are true. ## Input The first line contains integer number _A_ and the second line contains integer number _B_ (0 ≤ _A_, _B_ ≤ 264 - 1). ## Output The only output line should contain two integer non-negative numbers _X_ and _Y_. Print the only number _\-1_ if there is no answer. [samples]

按位异或（或按位模二加法）是一种二元运算，它等价于对操作数二进制表示中相同位置的每一位应用逻辑异或。换句话说，结果的二进制位等于 1，当且仅当操作数中对应位置的位不同。例如，若 #cf_span[X = 10910 = 11011012], #cf_span[Y = 4110 = 1010012]，则：编写一个程序，输入两个非负整数 #cf_span[A] 和 #cf_span[B]，找出两个非负整数 #cf_span[X] 和 #cf_span[Y]，满足以下条件：第一行包含整数 #cf_span[A]，第二行包含整数 #cf_span[B]（#cf_span[0 ≤ A, B ≤ 264 - 1]）。输出仅一行，包含两个非负整数 #cf_span[X] 和 #cf_span[Y]。若无解，请仅输出 _-1_。 ## Input 第一行包含整数 #cf_span[A]，第二行包含整数 #cf_span[B]（#cf_span[0 ≤ A, B ≤ 264 - 1]）。 ## Output 输出仅一行，包含两个非负整数 #cf_span[X] 和 #cf_span[Y]。若无解，请仅输出 _-1_。 [samples]

**Definitions** Let $ A, B \in \mathbb{Z}_{\geq 0} $ with $ 0 \leq A, B \leq 2^{64} - 1 $. We seek $ X, Y \in \mathbb{Z}_{\geq 0} $ such that: $$ X + Y = A \quad \text{and} \quad X \oplus Y = B $$ where $ \oplus $ denotes bitwise XOR. **Constraints** 1. $ 0 \leq A, B \leq 2^{64} - 1 $ 2. $ X, Y \geq 0 $ **Objective** Find $ X, Y \in \mathbb{Z}_{\geq 0} $ satisfying: $$ X + Y = A \quad \text{and} \quad X \oplus Y = B $$ If no such pair exists, output $-1$.

Samples

Input #1

142
76

Output #1

33 109

API Response (JSON)

{
  "problem": {
    "name": "D. Plus and xor",
    "description": {
      "content": "Bitwise exclusive OR (or bitwise addition modulo two) is a binary operation which is equivalent to applying logical exclusive OR to every pair of bits located on the same positions in binary notation ",
      "description_type": "Markdown"
    },
    "platform": "Codeforces",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "CF76D"
  },
  "statements": [
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      "statement_type": "Markdown",
      "content": "Bitwise exclusive OR (or bitwise addition modulo two) is a binary operation which is equivalent to applying logical exclusive OR to every pair of bits located on the same positions in binary notation ...",
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      "language": "English"
    },
    {
      "statement_type": "Markdown",
      "content": "按位异或（或按位模二加法）是一种二元运算，它等价于对操作数二进制表示中相同位置的每一位应用逻辑异或。换句话说，结果的二进制位等于 1，当且仅当操作数中对应位置的位不同。\n\n例如，若 #cf_span[X = 10910 = 11011012], #cf_span[Y = 4110 = 1010012]，则：\n\n编写一个程序，输入两个非负整数 #cf_span[A] 和 #cf_span[B]，找出...",
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      "content": "**Definitions**  \nLet $ A, B \\in \\mathbb{Z}_{\\geq 0} $ with $ 0 \\leq A, B \\leq 2^{64} - 1 $.  \nWe seek $ X, Y \\in \\mathbb{Z}_{\\geq 0} $ such that:  \n$$\nX + Y = A \\quad \\text{and} \\quad X \\oplus Y = B\n...",
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}

Full JSON Raw Segments