{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003eArchaeologists find an ancient string on a monument, but some characters have become hazy with the passage of time, and we only know the remain characters.\u003cbr\u003e\u003cbr\u003eNow archaeologists want to re-build the string, and know two rules:\u003cbr\u003e\u003cbr\u003e- there is no palindrome substring in the original string. \u003cb\u003eNote that a single character is not regarded as a palindrome string here\u003c/b\u003e. \u003cbr\u003e- the character set size of the original string is $K$.\u003cbr\u003e- $0 \\leq$ the character of the original string $\u0026lt; K$\u003cbr\u003e\u003cbr\u003ePlease calculate the number of original string which satisfy above rules.\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"First line contains an integer T, which indicates the number of test cases.\u003cbr\u003e\u003cbr\u003eEvery test case begins with three integers $N$, $K$ and $L$, which is the number of known characters, the character set size of the original string and the length of the original string.\u003cbr\u003e\u003cbr\u003eThen $N$ lines follow, the $i^{th}$ line contains two integers $p_i$ and $v_i$, means the position and value of $i^{th}$ known character.\u003cbr\u003e\u003cbr\u003eLimits\u003cbr\u003e$1 \\leq T \\leq 100$.\u003cbr\u003e$0 \\leq N \\leq 2000$.\u003cbr\u003e$1 \\leq K \\leq 10^9$.\u003cbr\u003e$max(1, N) \\leq L \\leq 10^9$.\u003cbr\u003e$0 \\leq p_i \u0026lt; p_{i+1} \u0026lt;L$.\u003cbr\u003e$0 \\leq v_i \u0026lt; K$\u003cbr\u003eFor 90\\% of the use cases, $N \\leq 10$ holds."}},{"title":"Output","value":{"format":"HTML","content":"For every test case, you should output \u003cb\u003e\u0027Case #x: y\u0027\u003c/b\u003e, where \u003cb\u003ex\u003c/b\u003e indicates the case number and counts from \u003cb\u003e1\u003c/b\u003e and \u003cb\u003ey\u003c/b\u003e is the result.\u003cbr\u003e\u003cbr\u003eBecause \u003cb\u003ey\u003c/b\u003e could be very large, just mod it with $10^9 + 7$. "}},{"title":"Sample","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\r\n0 3 4\r\n1 4 4\r\n1 1\r\n2 5 5\r\n1 1\r\n3 2\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase #1: 6\r\nCase #2: 12\r\nCase #3: 27\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}