{"raw_statement":[{"iden":"problem statement","content":"There are $N$ citizens in the Kingdom of Takahashi. Each citizen has a national ID number; the ID of the $i$\\-th citizen is $a_i$. Here, all $a_i$ are pairwise different.\nTakahashi has $K$ pieces of sweets. He has decided to hand out these pieces to the citizens in the following way until he has no more pieces.\n\n*   When he has $N$ or more pieces, hand out one piece to every citizen.\n*   Otherwise, let $K'$ be the number of pieces he has at the moment, and hand out one piece to each of the citizens with the $K'$ smallest IDs.\n\nWhen all pieces are handed out, how many pieces will the $i$\\-th citizen have?"},{"iden":"constraints","content":"*   $1 \\leq N \\leq 2 \\times 10^5$\n*   $1 \\leq K \\leq 10^{18}$\n*   $1 \\leq a_i \\leq 10^9$\n*   All $a_i$ are pairwise different.\n*   All values in input are integers."},{"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":"2 7\n1 8"},{"iden":"sample output 1","content":"4\n3\n\nTakahashi will hand out the pieces as follows.\n\n*   Hand out one piece to everyone, leaving Takhashi with $5$ pieces.\n*   Hand out one piece to everyone, leaving Takhashi with $3$ pieces.\n*   Hand out one piece to everyone, leaving Takhashi with $1$ piece.\n*   Hand out one piece to the $1$\\-st citizen, leaving Takhashi with no pieces.\n\nIn the end, the $1$\\-st citizen will receive $4$ pieces, and the $2$\\-nd citizen will receive $3$ pieces."},{"iden":"sample input 2","content":"1 3\n33"},{"iden":"sample output 2","content":"3\n\nSince there is just one citizen, Takahashi will hand out all pieces to that $1$\\-st citizen."},{"iden":"sample input 3","content":"7 1000000000000\n99 8 2 4 43 5 3"},{"iden":"sample output 3","content":"142857142857\n142857142857\n142857142858\n142857142857\n142857142857\n142857142857\n142857142857"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}