Codeforces Round 562 (Div. 2) |
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Finished |
Toad Ivan has $$$m$$$ pairs of integers, each integer is between $$$1$$$ and $$$n$$$, inclusive. The pairs are $$$(a_1, b_1), (a_2, b_2), \ldots, (a_m, b_m)$$$.
He asks you to check if there exist two integers $$$x$$$ and $$$y$$$ ($$$1 \leq x < y \leq n$$$) such that in each given pair at least one integer is equal to $$$x$$$ or $$$y$$$.
The first line contains two space-separated integers $$$n$$$ and $$$m$$$ ($$$2 \leq n \leq 300\,000$$$, $$$1 \leq m \leq 300\,000$$$) — the upper bound on the values of integers in the pairs, and the number of given pairs.
The next $$$m$$$ lines contain two integers each, the $$$i$$$-th of them contains two space-separated integers $$$a_i$$$ and $$$b_i$$$ ($$$1 \leq a_i, b_i \leq n, a_i \neq b_i$$$) — the integers in the $$$i$$$-th pair.
Output "YES" if there exist two integers $$$x$$$ and $$$y$$$ ($$$1 \leq x < y \leq n$$$) such that in each given pair at least one integer is equal to $$$x$$$ or $$$y$$$. Otherwise, print "NO". You can print each letter in any case (upper or lower).
4 6 1 2 1 3 1 4 2 3 2 4 3 4
NO
5 4 1 2 2 3 3 4 4 5
YES
300000 5 1 2 1 2 1 2 1 2 1 2
YES
In the first example, you can't choose any $$$x$$$, $$$y$$$ because for each such pair you can find a given pair where both numbers are different from chosen integers.
In the second example, you can choose $$$x=2$$$ and $$$y=4$$$.
In the third example, you can choose $$$x=1$$$ and $$$y=2$$$.
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