{"problem":{"name":"Camel and Oases","description":{"content":"There are $N$ oases on a number line. The coordinate of the $i$\\-th oases from the left is $x_i$. Camel hopes to visit all these oases. Initially, the volume of the hump on his back is $V$. When the v","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"agc012_e"},"statements":[{"statement_type":"Markdown","content":"There are $N$ oases on a number line. The coordinate of the $i$\\-th oases from the left is $x_i$.\nCamel hopes to visit all these oases. Initially, the volume of the hump on his back is $V$. When the volume of the hump is $v$, water of volume at most $v$ can be stored. Water is only supplied at oases. He can get as much water as he can store at a oasis, and the same oasis can be used any number of times.\nCamel can travel on the line by either walking or jumping:\n\n*   Walking over a distance of $d$ costs water of volume $d$ from the hump. A walk that leads to a negative amount of stored water cannot be done.\n*   Let $v$ be the amount of water stored at the moment. When $v>0$, Camel can jump to any point on the line of his choice. After this move, the volume of the hump becomes $v/2$ (rounded down to the nearest integer), and the amount of stored water becomes $0$.\n\nFor each of the oases, determine whether it is possible to start from that oasis and visit all the oases.\n\n## Constraints\n\n*   $2 ≤ N,V ≤ 2 × 10^5$\n*   $-10^9 ≤ x_1 < x_2 < ... < x_N ≤ 10^9$\n*   $V$ and $x_i$ are all integers.\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $V$\n$x_1$ $x_2$ $...$ $x_{N}$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"agc012_e","tags":[],"sample_group":[["3 2\n1 3 6","Possible\nPossible\nPossible\n\nIt is possible to start from the first oasis and visit all the oases, as follows:\n\n*   Walk from the first oasis to the second oasis. The amount of stored water becomes $0$.\n*   Get water at the second oasis. The amount of stored water becomes $2$.\n*   Jump from the second oasis to the third oasis. The amount of stored water becomes $0$, and the volume of the hump becomes $1$."],["7 2\n-10 -4 -2 0 2 4 10","Impossible\nPossible\nPossible\nPossible\nPossible\nPossible\nImpossible\n\nA oasis may be visited any number of times."],["16 19\n-49 -48 -33 -30 -21 -14 0 15 19 23 44 52 80 81 82 84","Possible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nPossible\nImpossible\nImpossible\nImpossible\nImpossible"]],"created_at":"2026-03-03 11:01:14"}}