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# Ulrich from 2019 travels to Winden 1953 to accomplish a secret mission.

INSTRUCTIONS TO CANDIDATES

Ulrich from 2019 travels to Winden 1953 to accomplish a secret mission. He travels using the popular Winden Caves. After he has finished his secret mission in Winden 1953, he now has to return to the 2019. He can travel to 2019 using the caves. However, the cops of Winden know that Ulrich is on the loose, and are attempting to stop him by spreading his picture to the police at their bus stop. You must help Ulrich escape Winden-1953 by determining which busses he should take to reach the caves. However, because the police are actively looking for him, Ulrich has decided that he cannot sit still at any one bus stop for too long. Thus you need to determine which busses he should take so that his layover is never too long. Input Format: Line 1: N M T

-N is the max label of any bus station (1 is the starting point, N is the destination outside the country). Ulrich always starts at station 1 at time 0.

- M is the number of bus rides which appear on the schedule.

-T is the max time Ulrich can spend at any one station without being caught by the Winden Police. Note that he is allowed to spend exactly T time steps at a station, but not a moment

more.

Next M Lines: ryti t2.

- is the station label where a bus will be leaving from

-y is the station label where this bus will arrive

-t is the time the bus will leave station z.

t2 is the time the bus will arrive at station y.

Output Format: "NO" if, no matter what busses Ulrich takes, he will be caught before reaching station N. "YES Tmin" if he can escape, where Tmin is the earliest possible time that he arrives at station N.

At the very start, Ulrich is at station 1, at time 0. Suppose that Ulrich arrives at station r at time t. He can move to station y if and only if:

- There is a bus going from a to y at time t1, where t1>t, but t1-t

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