{"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\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":"MD","content":"Judy studies at Imperial University of Texas (IUT). Instinct, the main football team of IUT, is participating in an Inter-University Football Tournament. Judy is really excited about the tournament and wants to be a part of the team.\n\nInstinct is formed of **N** players. The team might have players belonging to different departments. There are **M** departments in IUT, numbered from **1** to **M**. Each student belongs to only one department. Judy is in **X** department. For each department **i**, Judy knows **S\u003csub\u003ei\u003c/sub\u003e**, the number of students that play football from that department.\n\nJudy, being the best player from her department, got selected. Now she wants to know the probability of having at least one teammate that belongs to her department."}},{"title":"Input","value":{"format":"MD","content":"Input starts with three positive space-separated integers, **N (≤ 10\u003csup\u003e2\u003c/sup\u003e)**, **M (≤ 10\u003csup\u003e3\u003c/sup\u003e)**, and **X (≤ M)**.\nThe following line contains a list of **M** space-separated positive integers **S\u003csub\u003ei\u003c/sub\u003e (≤ 10\u003csup\u003e2\u003c/sup\u003e)**. Note that, **S\u003csub\u003eX\u003c/sub\u003e** includes Judy too."}},{"title":"Output","value":{"format":"MD","content":"Print the required probability. Absolute errors less than **10\u003csup\u003e-6\u003c/sup\u003e** will be ignored.\nHowever, if it\u0027s not possible to form a team, print **-1**."}},{"title":"Sample Input","value":{"format":"MD","content":"`3 2 1`\n`2 2`"}},{"title":"Sample Output","value":{"format":"MD","content":"`0.666667`"}}]}