{"trustable":true,"prependHtml":"\u003cstyle type\u003d\u0027text/css\u0027\u003e\n .input, .output {\n border: 1px solid #888888;\n }\n .output {\n margin-bottom: 1em;\n position: relative;\n top: -1px;\n }\n .output pre, .input pre {\n background-color: #EFEFEF;\n line-height: 1.25em;\n margin: 0;\n padding: 0.25em;\n }\n \u003c/style\u003e\n \u003clink rel\u003d\"stylesheet\" href\u003d\"//codeforces.org/s/96598/css/problem-statement.css\" type\u003d\"text/css\" /\u003e\n\u003cscript\u003e\n window.katexOptions \u003d {\n delimiters: [\n {left: \u0027$$$$$$\u0027, right: \u0027$$$$$$\u0027, display: true},\n {left: \u0027$$$\u0027, right: \u0027$$$\u0027, display: false},\n {left: \u0027$$\u0027, right: \u0027$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003e\"Duel!\"\u003c/p\u003e\u003cp\u003eBetting on the lovely princess Claris, the duel between Tokitsukaze and Quailty has started.\u003c/p\u003e\u003cp\u003eThere are $$$n$$$ cards in a row. Each card has two sides, one of which has color. At first, some of these cards are with color sides facing up and others are with color sides facing down. Then they take turns flipping cards, in which Tokitsukaze moves first. In each move, one should choose exactly $$$k$$$ consecutive cards and flip them to the same side, which means to make their color sides all face up or all face down. If all the color sides of these $$$n$$$ cards face the same direction after one\u0027s move, the one who takes this move will win.\u003c/p\u003e\u003cp\u003ePrincess Claris wants to know who will win the game if Tokitsukaze and Quailty are so clever that they won\u0027t make mistakes.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two integers $$$n$$$ and $$$k$$$ ($$$1 \\le k \\le n \\le 10^5$$$).\u003c/p\u003e\u003cp\u003eThe second line contains a single string of length $$$n$$$ that only consists of $$$0$$$ and $$$1$$$, representing the situation of these $$$n$$$ cards, where the color side of the $$$i$$$-th card faces up if the $$$i$$$-th character is $$$1$$$, or otherwise, it faces down and the $$$i$$$-th character is $$$0$$$.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eonce again\u003c/span\u003e\" (without quotes) if the total number of their moves can exceed $$$10^9$$$, which is considered a draw.\u003c/p\u003e\u003cp\u003eIn other cases, print \"\u003cspan class\u003d\"tex-font-style-tt\"\u003etokitsukaze\u003c/span\u003e\" (without quotes) if Tokitsukaze will win, or \"\u003cspan class\u003d\"tex-font-style-tt\"\u003equailty\u003c/span\u003e\" (without quotes) if Quailty will win.\u003c/p\u003e\u003cp\u003eNote that the output characters are case-sensitive, and any wrong spelling would be rejected.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4 2\n0101\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003equailty\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e6 1\n010101\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eonce again\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e6 5\n010101\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003etokitsukaze\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4 1\n0011\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eonce again\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003eIn the first example, no matter how Tokitsukaze moves, there would be three cards with color sides facing the same direction after her move, and Quailty can flip the last card to this direction and win.\u003c/p\u003e\u003cp\u003eIn the second example, no matter how Tokitsukaze moves, Quailty can choose the same card and flip back to the initial situation, which can allow the game to end in a draw.\u003c/p\u003e\u003cp\u003eIn the third example, Tokitsukaze can win by flipping the leftmost five cards up or flipping the rightmost five cards down.\u003c/p\u003e\u003cp\u003eThe fourth example can be explained in the same way as the second example does.\u003c/p\u003e"}}]}