Chemistry in Berland

题意翻译

某学生要做实验，需要$n$种材料。 第$i$种材料需要$a_ikg$，实验室里有$b_ikg$。 已知一些材料可以互相转化。形式化的说，对于$2\le i\le n$，每$k_ikg$材料$x_i(1\le x_i<i)$可以转化为$1kg$材料$i$，而每$1kg$材料$i$能转化为$1kg$材料$x_i$。材料间的转化数必须是整数。 若经过任意转化能满足需求，输出"YES"，否则输出"NO"。

题目描述

Igor is a post-graduate student of chemistry faculty in Berland State University (BerSU). He needs to conduct a complicated experiment to write his thesis, but laboratory of BerSU doesn't contain all the materials required for this experiment. Fortunately, chemical laws allow material transformations (yes, chemistry in Berland differs from ours). But the rules of transformation are a bit strange. Berland chemists are aware of $ n $ materials, numbered in the order they were discovered. Each material can be transformed into some other material (or vice versa). Formally, for each $ i $ $ (2<=i<=n) $ there exist two numbers $ x_{i} $ and $ k_{i} $ that denote a possible transformation: $ k_{i} $ kilograms of material $ x_{i} $ can be transformed into $ 1 $ kilogram of material $ i $ , and $ 1 $ kilogram of material $ i $ can be transformed into $ 1 $ kilogram of material $ x_{i} $ . Chemical processing equipment in BerSU allows only such transformation that the amount of resulting material is always an integer number of kilograms. For each $ i $ ( $ 1<=i<=n $ ) Igor knows that the experiment requires $ a_{i} $ kilograms of material $ i $ , and the laboratory contains $ b_{i} $ kilograms of this material. Is it possible to conduct an experiment after transforming some materials (or none)?

输入输出格式

输入格式

The first line contains one integer number $ n $ ( $ 1<=n<=10^{5} $ ) — the number of materials discovered by Berland chemists. The second line contains $ n $ integer numbers $ b_{1},b_{2}...\ b_{n} $ ( $ 1<=b_{i}<=10^{12} $ ) — supplies of BerSU laboratory. The third line contains $ n $ integer numbers $ a_{1},a_{2}...\ a_{n} $ ( $ 1<=a_{i}<=10^{12} $ ) — the amounts required for the experiment. Then $ n-1 $ lines follow. $ j $ -th of them contains two numbers $ x_{j+1} $ and $ k_{j+1} $ that denote transformation of $ (j+1) $ -th material ( $ 1<=x_{j+1}<=j,1<=k_{j+1}<=10^{9} $ ).

输出格式

Print YES if it is possible to conduct an experiment. Otherwise print NO.

输入输出样例

输入样例 #1

3
1 2 3
3 2 1
1 1
1 1

输出样例 #1

YES

输入样例 #2

3
3 2 1
1 2 3
1 1
1 2

输出样例 #2

NO