CF652E Pursuit For Artifacts

Johnny is playing a well-known computer game. The game are in some country, where the player can freely travel, pass quests and gain an experience. In that country there are $ n $ islands and $ m $ bridges between them, so you can travel from any island to any other. In the middle of some bridges are lying ancient powerful artifacts. Johnny is not interested in artifacts, but he can get some money by selling some artifact. At the start Johnny is in the island $ a $ and the artifact-dealer is in the island $ b $ (possibly they are on the same island). Johnny wants to find some artifact, come to the dealer and sell it. The only difficulty is that bridges are too old and destroying right after passing over them. Johnnie's character can't swim, fly and teleport, so the problem became too difficult. Note that Johnny can't pass the half of the bridge, collect the artifact and return to the same island. Determine if Johnny can find some artifact and sell it.

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