There are $$$n$$$ variables; let's denote the value of the $$$i$$$-th variable as $$$a_i$$$.

There are also $$$m$$$ operations which will be applied to these variables; the $$$i$$$-th operation is described by three integers $$$x_i, y_i, z_i$$$. When the $$$i$$$-th operation is applied, the variable $$$x_i$$$ gets assigned the following value: $$$\min(a_{x_i}, a_{y_i} + z_i)$$$.

Every operation will be applied exactly once, but their order is not fixed; they can be applied in any order.

Let's call a sequence of initial variable values $$$a_1, a_2, \dots, a_n$$$ stable, if no matter in which order we apply operations, the resulting values will be the same. If the resulting value of the $$$i$$$-th variable depends on the order of operations, then the sequence of initial variable values is called $$$i$$$-unstable.

You have to process $$$q$$$ queries. In each query, you will be given initial values $$$a_1, a_2, \dots, a_n$$$ and an integer $$$k$$$; before applying the operations, you can at most $$$k$$$ times choose a variable and decrease it by $$$1$$$. For every variable $$$i$$$, you have to independently determine if it is possible to transform the given values into an $$$i$$$-unstable sequence.

Input

The first line contains two integers $$$n$$$ and $$$m$$$ ($$$2 \le n \le 500$$$; $$$1 \le m \le 4 \cdot 10^5$$$) — the number of variables and operations, respectively.

Then, $$$m$$$ lines follow. The $$$i$$$-th of them contains three integers $$$x_i, y_i, z_i$$$ ($$$1 \le x_i, y_i \le n$$$; $$$x_i \ne y_i$$$; $$$0 \le z_i \le 10^5$$$) — the description of the $$$i$$$-th operation.

The next line contains one integer $$$q$$$ ($$$1 \le q \le 1000$$$) — the number of queries.

Each query consists of two lines:

the first line contains one integer $$$k$$$ ($$$0 \le k \le 10^9$$$) — the maximum number of times you can choose a variable and decrease it by $$$1$$$;
the second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le 10^9$$$) — the initial values of the variables.

Output

For each query, print a string of $$$n$$$ zeroes and/or ones. The $$$i$$$-th character should be 1 if it is possible to obtain an $$$i$$$-unstable sequence, or 0 otherwise.

Note

Consider the first example. If the initial variable values are $$$[20, 0, 15, 5]$$$, the resulting values will be $$$[6, 0, 5, 5]$$$ with any order of operations. Decreasing the variables $$$10$$$ times is not enough. However, if we can apply no more than $$$30$$$ changes, we can decrease the $$$1$$$-st variable by $$$2$$$, and the $$$4$$$-th variable by $$$25$$$, we get initial values equal to $$$[18, 0, 15, -20]$$$, and this sequence is $$$2$$$-unstable and $$$3$$$-unstable:

if you apply the operations in the order they are given, you will get $$$[-12, 0, 5, -20]$$$;
however, if you apply the operations in order $$$[3, 2, 4, 1, 5]$$$, you will get $$$[-12, -2, 5, -20]$$$;
and if you apply the operations in order $$$[3, 4, 5, 1, 2]$$$, you will get $$$[-12, -2, 3, -20]$$$.

Idx	Name	Rating
A	Race	800
B	Shrinking Array	1100
C	Coloring Game	1300
D	Reachability and Tree	1700
E	Tree Colorings	2200
F	Variables and Operations	2800

Educational Codeforces Round 180 (Rated for Div. 2)