{"raw_statement":[{"iden":"problem statement","content":"You are given an integer sequence $A=(A_1,A_2,\\ldots,A_N)$ of length $N$.\nPerform the following operation $M$ times:\n\n*   For each $i\\ (1\\leq i \\leq N)$, add $i$ to $A_i$. Then, find the minimum non-negative integer not contained in $A$."},{"iden":"constraints","content":"*   $1\\leq N,M \\leq 2\\times 10^5$\n*   $-10^9\\leq A_i\\leq 10^9$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $M$ \n$A_1$ $A_2$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"3 3\n-1 -1 -6"},{"iden":"sample output 1","content":"2\n2\n0\n\nThe $1$\\-st operation makes the sequence $A$\n$(-1 + 1, -1 +2 ,-6+3) = (0,1,-3).$\nThe minimum non-negative integer not contained in $A$ is $2$.\nThe $2$\\-nd operation makes the sequence $A$\n$(0 + 1, 1 +2 ,-3+3) = (1,3,0).$\nThe minimum non-negative integer not contained in $A$ is $2$.\nThe $3$\\-rd operation makes the sequence $A$\n$(1 + 1, 3 +2 ,0+3) = (2,5,3).$\nThe minimum non-negative integer not contained in $A$ is $0$."},{"iden":"sample input 2","content":"5 6\n-2 -2 -5 -7 -15"},{"iden":"sample output 2","content":"1\n3\n2\n0\n0\n0"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}