Lorenzo Von Matterhorn

题意翻译

巴尼住在$NYC$。$NYC$具有从$1$开始的正整数编号的无数个交叉点。在交叉点$i$和$2i$之间以及$i$和$2i+1$之间存在双向道路，对任意整数$i$都满足：在任意两点之间都有且只有一条最短路。 最初任何人都可以免费通过任何道路。但是后来发生了$q$个事件。有两种类型的事件: 1.政府制定新规。一项规则可以用三个整数表示：$v$,$u$和$w$。经过这次事件，点$u$到点$v$路径上的所有边增加$w$元路费。 2.巴尼从点$v$通过最短路移动到点$u$。 现在巴尼想知道，他的每一次移动需要花多少钱。

题目描述

Barney lives in NYC. NYC has infinite number of intersections numbered with positive integers starting from 1. There exists a bidirectional road between intersections $ i $ and $ 2i $ and another road between $ i $ and $ 2i+1 $ for every positive integer $ i $ . You can clearly see that there exists a unique shortest path between any two intersections. Initially anyone can pass any road for free. But since SlapsGiving is ahead of us, there will $ q $ consecutive events happen soon. There are two types of events: 1\. Government makes a new rule. A rule can be denoted by integers $ v $ , $ u $ and $ w $ . As the result of this action, the passing fee of all roads on the shortest path from $ u $ to $ v $ increases by $ w $ dollars. 2\. Barney starts moving from some intersection $ v $ and goes to intersection $ u $ where there's a girl he wants to cuddle (using his fake name Lorenzo Von Matterhorn). He always uses the shortest path (visiting minimum number of intersections or roads) between two intersections. Government needs your calculations. For each time Barney goes to cuddle a girl, you need to tell the government how much money he should pay (sum of passing fee of all roads he passes).

输入输出格式

输入格式

The first line of input contains a single integer $ q $ ( $ 1<=q<=1000 $ ). The next $ q $ lines contain the information about the events in chronological order. Each event is described in form $ 1 $ $ v $ $ u $ $ w $ if it's an event when government makes a new rule about increasing the passing fee of all roads on the shortest path from $ u $ to $ v $ by $ w $ dollars, or in form $ 2 $ $ v $ $ u $ if it's an event when Barnie goes to cuddle from the intersection $ v $ to the intersection $ u $ . $ 1<=v,u<=10^{18},v≠u,1<=w<=10^{9} $ states for every description line.

输出格式

For each event of second type print the sum of passing fee of all roads Barney passes in this event, in one line. Print the answers in chronological order of corresponding events.

输入输出样例

输入样例 #1

7
1 3 4 30
1 4 1 2
1 3 6 8
2 4 3
1 6 1 40
2 3 7
2 2 4

输出样例 #1

94
0
32

说明

In the example testcase: Here are the intersections used: 1. Intersections on the path are $ 3 $ , $ 1 $ , $ 2 $ and $ 4 $ . 2. Intersections on the path are $ 4 $ , $ 2 $ and $ 1 $ . 3. Intersections on the path are only $ 3 $ and $ 6 $ . 4. Intersections on the path are $ 4 $ , $ 2 $ , $ 1 $ and $ 3 $ . Passing fee of roads on the path are $ 32 $ , $ 32 $ and $ 30 $ in order. So answer equals to $ 32+32+30=94 $ . 5. Intersections on the path are $ 6 $ , $ 3 $ and $ 1 $ . 6. Intersections on the path are $ 3 $ and $ 7 $ . Passing fee of the road between them is $ 0 $ . 7. Intersections on the path are $ 2 $ and $ 4 $ . Passing fee of the road between them is $ 32 $ (increased by $ 30 $ in the first event and by $ 2 $ in the second).