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. 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 initi