{"problem":{"name":"Reversible Cards 2","description":{"content":"We have $N$ cards numbered $1$ to $N$.   Card $i$ has an integer $A_i$ written on the front and an integer $B_i$ written on the back. Here, $\\sum_{i=1}^N (A_i + B_i) = M$.   For each $k=0,1,2,...,M$, ","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":3000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"abc269_g"},"statements":[{"statement_type":"Markdown","content":"We have $N$ cards numbered $1$ to $N$.  \nCard $i$ has an integer $A_i$ written on the front and an integer $B_i$ written on the back. Here, $\\sum_{i=1}^N (A_i + B_i) = M$.  \nFor each $k=0,1,2,...,M$, solve the following problem.\n\n> The $N$ cards are arranged so that their front sides are visible. You may choose between $0$ and $N$ cards (inclusive) and flip them.  \n> To make the sum of the visible numbers equal to $k$, at least how many cards must be flipped? Print this number of cards.  \n> If there is no way to flip cards to make the sum of the visible numbers equal to $k$, print $-1$ instead.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $0 \\leq M \\leq 2 \\times 10^5$\n*   $0 \\leq A_i, B_i \\leq M$\n*   $\\sum_{i=1}^N (A_i + B_i) = M$\n*   All values in the input are integers.\n\n## Input\n\nThe input is given from Standard Input in the following format:\n\n$N$ $M$\n$A_1$ $B_1$\n$A_2$ $B_2$\n$\\vdots$ \n$A_N$ $B_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"abc269_g","tags":[],"sample_group":[["3 6\n0 2\n1 0\n0 3","1\n0\n2\n1\n1\n3\n2\n\nFor $k=0$, for instance, flipping just card $2$ makes the sum of the visible numbers $0+0+0=0$. This choice is optimal.  \nFor $k=5$, flipping all cards makes the sum of the visible numbers $2+0+3=5$. This choice is optimal."],["2 3\n1 1\n0 1","\\-1\n0\n1\n-1"],["5 12\n0 1\n0 3\n1 0\n0 5\n0 2","1\n0\n1\n1\n1\n2\n1\n2\n2\n2\n3\n3\n4"]],"created_at":"2026-03-03 11:01:14"}}