{"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":"Define a \u0027reduce\u0027 operation as replacing a number with the count of its 1 bits in its binary representation. \n\u003cbr\u003e\u003cbr\u003e\nGiven a binary number $n$, how many integers less than or equal to $n$ require $k$ \u0027reduce\u0027 operations to become 1? \n\u003cbr\u003e\u003cbr\u003e\nFor example, for the number 7, it takes 3 operations (7 -\u003e 3 -\u003e 2 -\u003e 1) to become 1.\n"}},{"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\n\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\n\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":"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\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":"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\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"}}]}