104. Material Composition

I'm a slow walker, but I never walk backwards.

Task Description

Write a program to determine whether we can use up all materials in making goods. There are three kinds of materials $A$, $B$, and $C$, and there are also three kinds of good, $D$, $E$, and $F$. To make a $D$ we need $DA$ units of material $A$, $DB$ units of material $B$, and $DC$ units of materials $C$. Similarly for $E$ we need $EA$, $EB$ and $EC$ units of materials $A$, $B$, $C$, and for $F$ we need $FA$, $FB$, and $FC$ units of materials $A$, $B$, and $C$. Now given the units of materials $A$, $B$, and $C$ available, could we make goods $D$, $E$ and $F$, and use up ALL materials? Note that we do not need to make every kind of goods.

Input

The first line of the input has $DA$, $DB$, and $DC$. The second line of the input has $EA$, $EB$, and $EC$, and the third line has $FA$, $FB$, and $FC$. Then the next line has $n$, the number of test cases. Each test case has $a$, $b$, and $c$ in a line, as the units of available material $A$, $B$ and $C$ in this test case. All numbers are integers between $1$ and $10$.

Output

The output has $n$ lines. If in a test case we can use up all materials, then output "yes\n". Otherwise output "no\n".

Sample Input

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

Sample Output

no
yes
yes
no
yes

Hint

Could you use recursion to transform this problem in to many smaller and similar problems?

Limitation

In this problem, the use of keyword for, while, goto, are forbidden.

Discussion