{"trustable":false,"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$$\u0027, display: true},\n {left: \u0027$\u0027, right: \u0027$\u0027, display: false}\n ]\n };\n\u003c/script\u003e\n","sections":[{"title":"Enunciado","value":{"format":"HTML","content":"\u003cp\u003eLetícia e Lucas estão trabalhando em um projeto envolvendo processamento de imagens e precisam de sua ajuda. Você recebe uma matriz composta por $$$2$$$ linhas e $$$n$$$ colunas. Cada célula dessa matriz deve ser colorida de preto ou branco.\u003c/p\u003e\n\u003cp\u003eDuas células são consideradas vizinhas se tiverem uma fronteira comum e compartilharem a mesma cor. Duas células $$$A$$$ e $$$B$$$ pertencem ao mesmo componente se forem vizinhas ou se houver um vizinho de $$$A$$$ que pertença ao mesmo componente de $$$B$$$.\u003c/p\u003e\n\u003cp\u003eUma matriz possui uma coloração \u003cspan class\u003d\"tex-font-style-it\"\u003eperfeita\u003c/span\u003e se a mesma tiver exatamente $$$k$$$ componentes.\u003c/p\u003e\n\u003cp\u003eA sua tarefa é ajudar Letícia e Lucas a contarem o número de matrizes \u003cspan class\u003d\"tex-font-style-it\"\u003eperfeitas\u003c/span\u003e que podem ser criadas. O número pode ser grande, então imprima a resposta módulo $$$998244353$$$.\u003c/p\u003e"}},{"title":"Entrada","value":{"format":"HTML","content":"\u003cp\u003eA única linha contém dois inteiros $$$n$$$ e $$$k$$$ ($$$1 \\le n \\le 1000$$$, $$$1 \\le k \\le 2n$$$) — o número de colunas em uma matriz e o número de componentes.\u003c/p\u003e"}},{"title":"Saída","value":{"format":"HTML","content":"\u003cp\u003eImprima um único inteiro — o número de matrizes \u003cspan class\u003d\"tex-font-style-it\"\u003eperfeitas\u003c/span\u003e que podem ser criadas módulo $$$998244353$$$.\u003c/p\u003e"}},{"title":"Caso de Teste 1","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eEntrada\u003c/th\u003e\n \u003cth\u003eSaída\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3 4\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e12\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Caso de Teste 2","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eEntrada\u003c/th\u003e\n \u003cth\u003eSaída\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Caso de Teste 3","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eEntrada\u003c/th\u003e\n \u003cth\u003eSaída\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e1 2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e2\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Exemplo","value":{"format":"HTML","content":"\u003cp\u003eA seguir tem um exemplo de uma matriz perfeita para o caso de teste $$$1$$$:\u003c/p\u003e\u003ccenter\u003e \u003cimg class\u003d\"tex-graphics\" src\u003d\"CDN_BASE_URL/12aef61342a340b71e8687f470af7cb1?v\u003d1723503620\" style\u003d\"max-width: 100.0%;max-height: 100.0%;\"\u003e \u003c/center\u003e"}}]}