{"raw_statement":[{"iden":"problem statement","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."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq K \\leq 2 \\times 10^5$\n*   $0 \\leq A_i \\leq N$"},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"5 1\n1 0 0 1 0"},{"iden":"sample output 1","content":"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 $2$."},{"iden":"sample input 2","content":"5 2\n1 0 0 1 0"},{"iden":"sample output 2","content":"3 3 4 4 3"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}