{"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\u003cscript\u003e window.katexOptions \u003d { disable: true }; \u003c/script\u003e\n\u003cscript type\u003d\"text/x-mathjax-config\"\u003e\n MathJax.Hub.Config({\n tex2jax: {\n inlineMath: [[\u0027$$$\u0027,\u0027$$$\u0027], [\u0027$\u0027,\u0027$\u0027]],\n displayMath: [[\u0027$$$$$$\u0027,\u0027$$$$$$\u0027], [\u0027$$\u0027,\u0027$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eAndi likes numbers and sequences, especially, sign sequences. A sign sequence is a sequence which consists of $$$-1$$$ and $$$1$$$. Andi is a curious person, thus, he wants to build a sign sequence which length is $$$N$$$ (the positions are numbered from $$$1$$$ to $$$N$$$, inclusive).\u003c/p\u003e\u003cp\u003eHowever, Andi also likes some challenges. Therefore, he prefilled some positions in the sequence with $$$-1$$$ or $$$1$$$ (the number in these positions cannot be changed). Andi also wants the sequence to fulfill $$$K$$$ constraints. For each constraint, there are 3 numbers: $$$A_i$$$, $$$B_i$$$, and $$$C_i$$$. This means that the sum of numbers which position is in the range $$$[A_i, B_i]$$$ (inclusive) must be at least $$$C_i$$$.\u003c/p\u003e\u003cp\u003eSounds confusing, right? It is not done yet. Since there can be many sequences that fulfill all the criteria above, Andi wants the sequence to be lexicographically smallest. Sequence $$$X$$$ is lexicographically smaller than sequence $$$Y$$$ if and only if there exists a position $$$i$$$ where $$$X_i \u0026lt; Y_i$$$ and $$$X_j \u003d Y_j$$$ for all $$$j \u0026lt; i$$$.\u003c/p\u003e\u003cp\u003eFind the sequence Andi wants.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eInput begins with a line containing two integers: $$$N$$$ $$$K$$$ ($$$1 \\le N \\le 100000$$$; $$$0 \\le K \\le 100000$$$) representing the length of the sequence and the number of constraints, respectively. The second line contains $$$N$$$ integers: $$$P_i$$$ ($$$-1 \\le P_i \\le 1$$$). If $$$P_i \u003d 0$$$, then the $$$i^{th}$$$ position in the sequence is not prefilled, otherwise the $$$i^{th}$$$ position in the sequence is prefilled by $$$P_i$$$. The next $$$K$$$ lines, each contains three integers: $$$A_i$$$ $$$B_i$$$ $$$C_i$$$ ($$$1 \\le A_i \\le B_i \\le N$$$; $$$-N \\le C_i \\le N$$$) representing the $$$i^{th}$$$ constraint.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput contains $$$N$$$ integers (each separated by a single space) in a line representing the sequence that Andi wants if there exists such sequence, or \"\u003cspan class\u003d\"tex-font-style-tt\"\u003eImpossible\u003c/span\u003e\" (without quotes) otherwise.\u003c/p\u003e"}},{"title":"Examples","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3 2\n0 0 0\n1 2 2\n2 3 -1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1 1 -1\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e3 2\n0 -1 0\n1 2 2\n2 3 -1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eImpossible\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003e\u003cspan class\u003d\"tex-font-style-it\"\u003eExplanation for the sample input/output #1\u003c/span\u003e\u003c/p\u003e\u003cp\u003eBoth sequences $$$[1, 1, -1]$$$ and $$$[1, 1, 1]$$$ satisfy the prefilled conditions and the given $$$K$$$ constraints. The former is lexicographically smaller.\u003c/p\u003e\u003cp\u003e\u003cspan class\u003d\"tex-font-style-it\"\u003eExplanation for the sample input/output #2\u003c/span\u003e\u003c/p\u003e\u003cp\u003eThe second position is already prefilled with $$$-1$$$, so it is impossible to fulfill the first constraint. There is no valid sequence in this case.\u003c/p\u003e"}}]}