Electrification

Ellen is designing the light-management system for a luxury hotel room. The room has n switches and m lamps.

The room designers assigned each lamp a set of switches. A lamp changes its state (it turns on if it was off, and turns off if it was on) every time one of the switches assigned to it is flipped. A lamp never reacts to a switch that is not assigned to it.

Initially every switch is off and every lamp is off. Ellen then flips a sequence of switches, one at a time. After all of the flips have been performed, report the final state of every lamp.

The first line contains two integers n and m — the number of switches and the number of lamps (1 ≤ n, m ≤ 10).

Each of the next n lines contains m characters. The j-th character of the i-th line is 1 if switch i is assigned to lamp j, and 0 otherwise. Every lamp is assigned at least one switch, and every switch is assigned to at least one lamp.

The next line contains an integer q — the number of switch flips (0 ≤ q ≤ 1000).

The following line lists q integers s_1, s_2, …, s_q (1 ≤ s_k ≤ n): the switches that are flipped, in the given order. When q = 0 this line is empty or omitted.

Print a single line of m characters. The j-th character must be 1 if lamp j is on after all the flips have been performed, and 0 otherwise.