{"raw_statement":[{"iden":"problem statement","content":"The Republic of ARC has $N$ citizens, all of whom play competitive programming. Each citizen is given a dan _(grade)_ which is $1$, $2$, $\\ldots$, or $K$, according to their skill.\nA national census has revealed that there are exactly $A_i$ citizens with dan $i$. To make this data easier to understand, the king has decided to describe the country as if it were a village of $M$ people.\nSet the number of people with dan $i$ in the village, $B_i$, so that $\\max_i\\left|\\frac{B_i}{M} - \\frac{A_i}{N}\\right|$ is minimized, while satisfying the following:\n\n*   each $B_i$ is a non-negative integer, satisfying $\\sum_{i=1}^K B_i = M$.\n\nPrint one such way to set $B = (B_1, B_2, \\ldots, B_K)$."},{"iden":"constraints","content":"*   $1\\leq K\\leq 10^5$\n*   $1\\leq N, M\\leq 10^9$\n*   Each $A_i$ is a non-negative integer satisfying $\\sum_{i=1}^K A_i = N$."},{"iden":"input","content":"Input is given from Standard Input in the following format:\n\n$K$ $N$ $M$\n$A_1$ $A_2$ $\\ldots$ $A_K$"},{"iden":"sample input 1","content":"3 7 20\n1 2 4"},{"iden":"sample output 1","content":"3 6 11\n\nIn this output, we have $\\max_i\\left|\\frac{B_i}{M} - \\frac{A_i}{N}\\right| = \\max\\left(\\left|\\frac{3}{20}-\\frac{1}{7}\\right|, \\left|\\frac{6}{20}-\\frac{2}{7}\\right|, \\left|\\frac{11}{20}-\\frac{4}{7}\\right|\\right) = \\max\\left(\\frac{1}{140}, \\frac{1}{70}, \\frac{3}{140}\\right) = \\frac{3}{140}$."},{"iden":"sample input 2","content":"3 3 100\n1 1 1"},{"iden":"sample output 2","content":"34 33 33\n\nNote that $B_1 = B_2 = B_3 = 33$ does not satisfy the requirement, since the sum must be $M = 100$.\nIn this sample, other than `34 33 33`, printing `33 34 33` or `33 33 34` will also be accepted."},{"iden":"sample input 3","content":"6 10006 10\n10000 3 2 1 0 0"},{"iden":"sample output 3","content":"10 0 0 0 0 0"},{"iden":"sample input 4","content":"7 78314 1000\n53515 10620 7271 3817 1910 956 225"},{"iden":"sample output 4","content":"683 136 93 49 24 12 3"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}