{"raw_statement":[{"iden":"statement","content":"Alice likes snow a lot! Unfortunately, this year's winter is already over, and she can't expect to have any more of it. Bob has thus bought her a gift — a large snow maker. He plans to make some amount of snow every day. On day _i_ he will make a pile of snow of volume _V__i_ and put it in her garden.\n\nEach day, every pile will shrink a little due to melting. More precisely, when the temperature on a given day is _T__i_, each pile will reduce its volume by _T__i_. If this would reduce the volume of a pile to or below zero, it disappears forever. All snow piles are independent of each other.\n\nNote that the pile made on day _i_ already loses part of its volume on the same day. In an extreme case, this may mean that there are no piles left at the end of a particular day.\n\nYou are given the initial pile sizes and the temperature on each day. Determine the total volume of snow melted on each day."},{"iden":"input","content":"The first line contains a single integer _N_ (1 ≤ _N_ ≤ 105) — the number of days.\n\nThe second line contains _N_ integers _V_1, _V_2, ..., _V__N_ (0 ≤ _V__i_ ≤ 109), where _V__i_ is the initial size of a snow pile made on the day _i_.\n\nThe third line contains _N_ integers _T_1, _T_2, ..., _T__N_ (0 ≤ _T__i_ ≤ 109), where _T__i_ is the temperature on the day _i_."},{"iden":"output","content":"Output a single line with _N_ integers, where the _i_\\-th integer represents the total volume of snow melted on day _i_."},{"iden":"examples","content":"Input\n\n3\n10 10 5\n5 7 2\n\nOutput\n\n5 12 4\n\nInput\n\n5\n30 25 20 15 10\n9 10 12 4 13\n\nOutput\n\n9 20 35 11 25"},{"iden":"note","content":"In the first sample, Bob first makes a snow pile of volume 10, which melts to the size of 5 on the same day. On the second day, he makes another pile of size 10. Since it is a bit warmer than the day before, the first pile disappears completely while the second pile shrinks to 3. At the end of the second day, he has only a single pile of size 3. On the third day he makes a smaller pile than usual, but as the temperature dropped too, both piles survive till the end of the day."}],"translated_statement":null,"sample_group":[],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}