codeforces round 512 F. Putting Boxes Together 树状数组维护区间加权平均数

F. Putting Boxes Together

time limit per test

2.5 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

There is an infinite line consisting of cells. There are $\mathrm{nn boxes\; in\; some\; cells\; of\; this\; line.\; The ii-th\; box\; stands\; in\; the\; cell aiai and\; has\; weight wiwi.\; All aiai are\; distinct,\; moreover, ai-1<aiai-1ii.}$

You would like to put together some boxes. Putting together boxes with indices in the segment $[l,r][l,r] means\; that\; you\; will\; move\; some\; of\; them\; in\; such\; a\; way\; that\; their positions will\; form\; some\; segment [x,x+(r-l)][x,x+(r-l)].$

In one step you can move any box to a neighboring cell if it isn't occupied by another box (i.e. you can choose $\mathrm{ii and\; change aiai by 11,\; all\; positions\; should\; remain\; distinct).\; You\; spend wiwi units\; of\; energy\; moving\; the\; box ii by\; one\; cell.\; You\; can\; move\; any\; box\; any\; number\; of\; times,\; in\; arbitrary\; order.}$

Sometimes weights of some boxes change, so you have queries of two types:

1. $\mathrm{idid nwnw —\; weight widwid of\; the\; box idid becomes nwnw.}$
2. $\mathrm{ll rr —\; you\; should\; compute\; the\; minimum\; total\; energy\; needed\; to\; put\; together\; boxes\; with\; indices\; in [l,r][l,r].\; Since\; the\; answer\; can\; be\; rather\; big,\; print\; the\; remainder\; it\; gives\; when\; divided\; by 1000000007=109+71000000007=109+7.\; Note\; that\; the\; boxes\; are\; not\; moved\; during\; the\; query,\; you\; only\; should\; compute\; the\; answer.}$

Note that you should minimize the answer, not its remainder modulo ${\mathrm{109+7109+7.\; So\; if\; you\; have\; two\; possible\; answers 2\cdot 109+132\cdot 109+13and 2\cdot 109+142\cdot 109+14,\; you\; should\; choose\; the\; first\; one\; and\; print 109+6109+6,\; even\; though\; the\; remainder\; of\; the\; second\; answer\; is 00.}}^{}$

Input

The first line contains two integers $\mathrm{nn and qq (1\le n,q\le 2\cdot 1051\le n,q\le 2\cdot 105)\; —\; the\; number\; of\; boxes\; and\; the\; number\; of\; queries.}$

The second line contains $\mathrm{nn integers a1,a2,\dots ana1,a2,\dots an (1\le ai\le 1091\le ai\le 109)\; —\; the\; positions\; of\; the\; boxes.\; All aiai are\; distinct, ai-1<aiai-1ii.}$

The third line contains $\mathrm{nn integers w1,w2,\dots wnw1,w2,\dots wn (1\le wi\le 1091\le wi\le 109)\; —\; the\; initial\; weights\; of\; the\; boxes.}$

Next $\mathrm{qq lines\; describe\; queries,\; one\; query\; per\; line.}$

Each query is described in a single line, containing two integers $\mathrm{xx and yy.\; If x<0x<0,\; then\; this\; query\; is\; of\; the\; first\; type,\; where id=-xid=-x, nw=ynw=y (1\le id\le n1\le id\le n, 1\le nw\le 1091\le nw\le 109).\; If x>0x>0,\; then\; the\; query\; is\; of\; the\; second\; type,\; where l=xl=x and r=yr=y (1\le lj\le rj\le n1\le lj\le rj\le n). xx can\; not\; be\; equal\; to 00.}$

Output

For each query of the second type print the answer on a separate line. Since answer can be large, print the remainder it gives when divided by $\mathrm{1000000007=109+71000000007=109+7.}$

Example

input

Copy

5 8
1 2 6 7 10
1 1 1 1 2
1 1
1 5
1 3
3 5
-3 5
-1 10
1 4
2 5

output

Copy

0
10
3
4
18
7

Note

Let's go through queries of the example:

1. $\mathrm{1 11 1 —\; there\; is\; only\; one\; box\; so\; we\; don\text{'}t\; need\; to\; move\; anything.}$
2. $\mathrm{1 51 5 —\; we\; can\; move\; boxes\; to\; segment [4,8][4,8]: 1\cdot |1-4|+1\cdot |2-5|+1\cdot |6-6|+1\cdot |7-7|+2\cdot |10-8|=101\cdot |1-4|+1\cdot |2-5|+1\cdot |6-6|+1\cdot |7-7|+2\cdot |10-8|=10.}$
3. $\mathrm{1 31 3 —\; we\; can\; move\; boxes\; to\; segment [1,3][1,3].}$
4. $\mathrm{3 53 5 —\; we\; can\; move\; boxes\; to\; segment [7,9][7,9].}$
5. $-3 5-3 5 — w3w3 is\; changed\; from 11 to 55.$
6. $-1 10-1 10 — w1w1 is\; changed\; from 11 to 1010.\; The\; weights\; are\; now\; equal\; to w=[10,1,5,1,2]w=[10,1,5,1,2].$
7. $\mathrm{1 41 4 —\; we\; can\; move\; boxes\; to\; segment [1,4][1,4].}$
8. $\mathrm{2 52 5 —\; we\; can\; move\; boxes\; to\; segment [5,8][5,8].}$

$\mathrm{思路：}$

树状数组加二分

  1 #include 
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  5 #include 
  6 #include 
  7 #include <string>
  8 #include 
  9 #include 
 10 #include 
 11 #include 
 12 #include 
 13 #include <set>
 14 #include 

View Code

 

转载于:https://www.cnblogs.com/BIGTOM/p/9738058.html