{"raw_statement":[{"iden":"problem statement","content":"You are given non-negative integers $a$, $b$, and $C$. Determine if there is a pair of non-negative integers $(X, Y)$ that satisfies all of the following five conditions. If such a pair exists, print one.\n\n*   $0 \\leq X < 2^{60}$\n*   $0 \\leq Y < 2^{60}$\n*   $\\operatorname{popcount}(X) = a$\n*   $\\operatorname{popcount}(Y) = b$\n*   $X \\oplus Y = C$\n\nHere, $\\oplus$ denotes the bitwise XOR.\nIf multiple pairs $(X, Y)$ satisfy the conditions, you may print any of them.\nWhat is popcount?For a non-negative integer $x$, the popcount of $x$ is the number of $1$s in the binary representation of $x$. More precisely, for a non-negative integer $x$ such that $\\displaystyle x=\\sum _ {i=0} ^ \\infty b _ i2 ^ i\\ (b _ i\\in\\lbrace0,1\\rbrace)$, we have $\\displaystyle\\operatorname{popcount}(x)=\\sum _ {i=0} ^ \\infty b _ i$.\nFor example, $13$ in binary is `1101`, so $\\operatorname{popcount}(13)=3$. What is bitwise XOR?For non-negative integers $x, y$, the bitwise exclusive OR $x \\oplus y$ is defined as follows.\n\n*   The $2^k$'s place $\\ (k\\geq0)$ in the binary representation of $x \\oplus y$ is $1$ if exactly one of the $2^k$'s places $\\ (k\\geq0)$ in the binary representations of $x$ and $y$ is $1$, and $0$ otherwise.\n\nFor example, $9$ and $3$ in binary are `1001` and `0011`, respectively, so $9 \\oplus 3 = 10$ (in binary, `1010`)."},{"iden":"constraints","content":"*   $0 \\leq a \\leq 60$\n*   $0 \\leq b \\leq 60$\n*   $0 \\leq C < 2^{60}$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$a$ $b$ $C$"},{"iden":"sample input 1","content":"3 4 7"},{"iden":"sample output 1","content":"28 27\n\nThe pair $(X, Y) = (28, 27)$ satisfies the conditions. Here, $X$ and $Y$ in binary are `11100` and `11011`, respectively.\n\n*   $X$ in binary is `11100`, so $\\operatorname{popcount}(X) = 3$.\n*   $Y$ in binary is `11011`, so $\\operatorname{popcount}(Y) = 4$.\n*   $X \\oplus Y$ in binary is `00111`, so $X \\oplus Y = 7$.\n\nIf multiple pairs of non-negative integers satisfy the conditions, you may print any of them, so printing `42 45`, for example, would also be accepted."},{"iden":"sample input 2","content":"34 56 998244353"},{"iden":"sample output 2","content":"\\-1\n\nNo pair of non-negative integers satisfies the conditions."},{"iden":"sample input 3","content":"39 47 530423800524412070"},{"iden":"sample output 3","content":"540431255696862041 10008854347644927\n\nNote that the values to be printed may not fit in $32$\\-bit integers."}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}