{"raw_statement":[{"iden":"problem statement","content":"There are $N$ baskets numbered $1, 2, \\ldots, N$ arranged in a circle.  \nFor each $1\\leq i \\leq N-1$, basket $i+1$ is to the immediate right of basket $i$, and basket $1$ is to the immediate right of basket $N$.\nBasket $i$ now contains $A_i$ apples.\nTakahashi starts in front of basket $1$ and repeats the following action.\n\n*   If the basket he is facing contains an apple, take one and eat it. Then, regardless of whether he has eaten an apple now, go on to the next basket to the immediate right.\n\nFind the number of apples remaining in each basket when Takahashi has eaten exactly $K$ apples in total."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 10^5$\n*   $0 \\leq A_i \\leq 10^{12}$\n*   $1 \\leq K \\leq 10^{12}$\n*   There are at least $K$ apples in total. That is, $\\sum_{i=1}^{N}A_i\\geq K$.\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $K$\n$A_1$ $A_2$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"3 3\n1 3 0"},{"iden":"sample output 1","content":"0 1 0 \n\nTakahashi will do the following.\n\n*   Basket $1$, which he is facing, contains an apple, so he takes one and eats it. Then, he goes on to basket $2$. Now, the baskets have $0,3,0$ apples.\n*   Basket $2$, which he is facing, contains an apple, so he takes one and eats it. Then, he goes on to basket $3$. Now, the baskets have $0,2,0$ apples.\n*   Basket $3$, which he is facing, contains no apple. Then, he goes on to basket $1$. Now, the baskets have $0,2,0$ apples.\n*   Basket $1$, which he is facing, contains no apple. Then, he goes on to basket $2$. Now, the baskets have $0,2,0$ apples.\n*   Basket $2$, which he is facing, contains an apple, so he takes one and eats it. Then, he goes on to basket $3$. Now, the baskets have $0,1,0$ apple(s)."},{"iden":"sample input 2","content":"2 1000000000000\n1000000000000 1000000000000"},{"iden":"sample output 2","content":"500000000000 500000000000"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}