Lighting Optimization Challenge

You are given N rooms, each with a switch that can be either ON or OFF. The initial state of all switches is represented by a binary string state of length N (where '1' indicates the switch is ON and '0' indicates it is OFF). Your task is to determine if it is possible to achieve a configuration where exactly one switch is ON and all other switches are OFF, using at most K toggle operations. In a single toggle, you can change the state of one switch.

Note: If no switches are ON initially, it is impossible to meet the requirement.

Mathematical Formulation:

Let \( c = \) number of switches that are initially ON. To achieve exactly one ON switch, you need to toggle \( c - 1 \) of the currently ON switches to OFF. The condition for success is:

[ c \ge 1 \quad \text{and} \quad c - 1 \le K ]

inputFormat

The input is given via standard input in the following format:

N
state
K

Where:

• N is an integer representing the number of rooms (and switches).
• state is a binary string of length N representing the initial state of the switches.
• K is an integer representing the maximum number of toggle operations allowed.

outputFormat

Output via standard output a single string: YES if it is possible to achieve exactly one switch ON (and all others OFF) within at most K toggles; otherwise, output NO.

## sample

5
11001
3

YES