{"problem":{"name":"Lamps","description":{"content":"We have $N$ bulbs arranged on a number line, numbered $1$ to $N$ from left to right. Bulb $i$ is at coordinate $i$. Each bulb has a non-negative integer parameter called intensity. When there is a bul","description_type":"Markdown"},"platform":"AtCoder","limit":{"time_limit":2000,"memory_limit":262144},"difficulty":"None","is_remote":true,"is_sync":true,"sync_url":null,"sign":"tokiomarine2020_c"},"statements":[{"statement_type":"Markdown","content":"We have $N$ bulbs arranged on a number line, numbered $1$ to $N$ from left to right. Bulb $i$ is at coordinate $i$.\nEach bulb has a non-negative integer parameter called intensity. When there is a bulb of intensity $d$ at coordinate $x$, the bulb illuminates the segment from coordinate $x-d-0.5$ to $x+d+0.5$. Initially, the intensity of Bulb $i$ is $A_i$. We will now do the following operation $K$ times in a row:\n\n*   For each integer $i$ between $1$ and $N$ (inclusive), let $B_i$ be the number of bulbs illuminating coordinate $i$. Then, change the intensity of each bulb $i$ to $B_i$.\n\nFind the intensity of each bulb after the $K$ operations.\n\n## Constraints\n\n*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq K \\leq 2 \\times 10^5$\n*   $0 \\leq A_i \\leq N$\n\n## Input\n\nInput is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\ldots$ $A_N$\n\n[samples]","is_translate":false,"language":"English"}],"meta":{"iden":"tokiomarine2020_c","tags":[],"sample_group":[["5 1\n1 0 0 1 0","1 2 2 1 2 \n\nInitially, only Bulb $1$ illuminates coordinate $1$, so the intensity of Bulb $1$ becomes $1$ after the operation. Similarly, the bulbs initially illuminating coordinate $2$ are Bulb $1$ and $2$, so the intensity of Bulb $2$ becomes $2$."],["5 2\n1 0 0 1 0","3 3 4 4 3"]],"created_at":"2026-03-03 11:01:13"}}