{"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\u003eThe Travelling Salesman spends a lot of time travelling so he tends to get bored. To pass time, he likes to perform operations on numbers. One such operation is to take a positive integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e and reduce it to the number of bits set to \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e in the binary representation of \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ex\u003c/i\u003e\u003c/span\u003e. For example for number \u003cspan class\u003d\"tex-span\"\u003e13\u003c/span\u003e it\u0027s true that \u003cspan class\u003d\"tex-span\"\u003e13\u003csub class\u003d\"lower-index\"\u003e10\u003c/sub\u003e \u003d 1101\u003csub class\u003d\"lower-index\"\u003e2\u003c/sub\u003e\u003c/span\u003e, so it has \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e bits set and \u003cspan class\u003d\"tex-span\"\u003e13\u003c/span\u003e will be reduced to \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e in one operation.\u003c/p\u003e\u003cp\u003eHe calls a number \u003cspan class\u003d\"tex-font-style-it\"\u003especial\u003c/span\u003e if the minimum number of operations to reduce it to \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e is \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eHe wants to find out how many special numbers exist which are not greater than \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e. Please help the Travelling Salesman, as he is about to reach his destination!\u003c/p\u003e\u003cp\u003eSince the answer can be large, output it modulo \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e.\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003eThe first line contains integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e1 ≤ \u003ci\u003en\u003c/i\u003e \u0026lt; 2\u003csup class\u003d\"upper-index\"\u003e1000\u003c/sup\u003e\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe second line contains integer \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003ek\u003c/i\u003e\u003c/span\u003e (\u003cspan class\u003d\"tex-span\"\u003e0 ≤ \u003ci\u003ek\u003c/i\u003e ≤ 1000\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eNote that \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e is given in its binary representation without any leading zeros.\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003eOutput a single integer\u0026nbsp;— the number of special numbers not greater than \u003cspan class\u003d\"tex-span\"\u003e\u003ci\u003en\u003c/i\u003e\u003c/span\u003e, modulo \u003cspan class\u003d\"tex-span\"\u003e10\u003csup class\u003d\"upper-index\"\u003e9\u003c/sup\u003e + 7\u003c/span\u003e.\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\u003e110\n2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\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\u003e111111011\n2\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e169\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\u003eIn the first sample, the three special numbers are \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e5\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e6\u003c/span\u003e. They get reduced to \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e in one operation (since there are two set bits in each of \u003cspan class\u003d\"tex-span\"\u003e3\u003c/span\u003e, \u003cspan class\u003d\"tex-span\"\u003e5\u003c/span\u003e and \u003cspan class\u003d\"tex-span\"\u003e6\u003c/span\u003e) and then to \u003cspan class\u003d\"tex-span\"\u003e1\u003c/span\u003e in one more operation (since there is only one set bit in \u003cspan class\u003d\"tex-span\"\u003e2\u003c/span\u003e).\u003c/p\u003e"}}]}