{"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\u003eAlice and Bob are playing a game with a string of characters, with Alice going first. The string consists \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e characters, each of which is one of the first \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e letters of the alphabet. On a player’s turn, they can either arbitrarily permute the characters in the words, or delete exactly one character in the word (if there is at least one character). In addition, their resulting word cannot have appeared before throughout the entire game. The player unable to make a valid move loses the game.\u003c/p\u003e\u003cp\u003eGiven \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e, \u003ci\u003ek\u003c/i\u003e, \u003ci\u003ep\u003c/i\u003e\u003c/span\u003e, find the number of words with exactly \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e characters consisting of the first \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e letters of the alphabet such that Alice will win if both Alice and Bob play optimally. Return this number modulo the prime number \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line of input will contain three integers \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e, \u003ci\u003ek\u003c/i\u003e, \u003ci\u003ep\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e ≤ 250 000\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003ek\u003c/i\u003e ≤ 26\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e8\u003c/sup\u003e ≤ \u003ci\u003ep\u003c/i\u003e ≤ 10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 100\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e will be prime).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint a single integer, the number of winning words for Alice, modulo \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ep\u003c/i\u003e\u003c/span\u003e.\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 100000007\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e14\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\u003eThere are 14 strings that that Alice can win with. For example, some strings are \"bbaa\" and \"baaa\". Alice will lose on strings like \"aaaa\" or \"bbbb\".\u003c/p\u003e"}}]}