{"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":"HTML","content":"\u003cp\u003eBowen traveled and spent all his money. Bowen\u0027s friend introduced Bowen to a job teaching algorithms to kids at school. Before starting, the school gave Bowen a problem, in order to test whether Bowen was good enough to teach algorithms to children.\u003c/p\u003e\n\u003cp\u003eFor a string $s$ of length $n$ and containing only lowercase letters, a substring $p$ of this string is known. Some of the positions (and possibly all) where this substring appears in the original string $s$ has already known.\u003c/p\u003e\n\u003cp\u003eFind the number of possible solutions to the original string $s$. The answer may be large, output the result of modulo $10^9 + 7$.\u003c/p\u003e\n\u003cp\u003eBowen reads the problem and realizes that he doesn\u0027t know it, so he wants to ask you to help him solve it.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains two integers $n$ and $m$, the length of $s$ and the number of position of $p$ already known $(1 \\leq n \\leq 10^6 , 0 \\leq m ≤ n - |p| + 1)$.\u003c/p\u003e\n\u003cp\u003eThe second line contains string $p$ $(1 \\leq |p| \\leq n)$.\u003c/p\u003e\n\u003cp\u003eThe next line contains m space separated integers $y_1, y_2, ..., y_m$, the position of $p$ $(1 \\leq y_1 \u003c y_2 \u003c ... \u003c y_m ≤ n - |p| + 1)$.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003ePrint the answer modulo $10^9 + 7$, if the string s cannot exist, output 0.\u003c/p\u003e"}},{"title":"Sample 1","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\u003e6 2\naba\n1 3\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e26\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}},{"title":"Sample 2","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\u003e20 2\nabababab\n1 6\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}