{"problem":{"name":"XXOR","description":{"content":"You are given $N$ non-negative integers $A_1, A_2, ..., A_N$ and another non-negative integer $K$. For a integer $X$ between $0$ and $K$ (inclusive), let $f(X) = (X$ XOR $A_1)$ $+$ $(X$ XOR $A_2)$ $+$","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc117_d"},"statements":[{"statement_type":"Markdown","content":"You are given $N$ non-negative integers $A_1, A_2, ..., A_N$ and another non-negative integer $K$.\nFor a integer $X$ between $0$ and $K$ (inclusive), let $f(X) = (X$ XOR $A_1)$ $+$ $(X$ XOR $A_2)$ $+$ $...$ $+$ $(X$ XOR $A_N)$.\nHere, for non-negative integers $a$ and $b$, $a$ XOR $b$ denotes the bitwise exclusive OR of $a$ and $b$.\nFind the maximum value of $f$.\n\nWhat is XOR?\n\nThe bitwise exclusive OR of $a$ and $b$, $X$, is defined as follows:\n\n*   When $X$ is written in base two, the digit in the $2^k$'s place ($k \\geq 0$) is $1$ if, when written in base two, exactly one of $A$ and $B$ has $1$ in the $2^k$'s place, and $0$ otherwise.\n\nFor example, $3$ XOR $5 = 6$. (When written in base two: $011$ XOR $101 = 110$.)\n\n## Constraints\n\n*   All values in input are integers.\n*   $1 \\leq N \\leq 10^5$\n*   $0 \\leq K \\leq 10^{12}$\n*   $0 \\leq A_i \\leq 10^{12}$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $...$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc117_d","tags":[],"sample_group":[["3 7\n1 6 3","14\n\nThe maximum value is: $f(4) = (4$ XOR $1) + (4$ XOR $6) + (4$ XOR $3) = 5 + 2 + 7 = 14$."],["4 9\n7 4 0 3","46"],["1 0\n1000000000000","1000000000000"]],"created_at":"2026-03-03 11:01:14"}}