{"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$$\u0027]]\n }\n });\n\u003c/script\u003e\n\u003cscript type\u003d\"text/javascript\" async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS_HTML-full\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cp\u003eBeast非常喜欢正整数序列,他提出了一个问题。\u003c/p\u003e\n\u003cp\u003e他认为一个正整数是\u003cspan class\u003d\"tex-font-style-it\"\u003e特殊的\u003c/span\u003e,如果这个数被可以写成 $$$n$$$的不同非负数幂次之和. 比如说,当 $$$n \u003d 4$$$的时候, $$$17$$$是特殊的, 因为$$$4^0 + 4^2 \u003d 1 + 16 \u003d 17$$$\u003c/p\u003e\n\u003cp\u003eBeast要求你帮助他找到第$$$k$$$个特殊的数字(这些数按升序排序). 因为答案很大,因此需要对$$$10^9+7$$$取模\u003c/p\u003e"}},{"title":"Input","value":{"format":"HTML","content":"\u003cp\u003e第一行是测试样例的数量,$$$t$$$ ($$$1 \\le t \\le 10^4$$$)\u003c/p\u003e\n\u003cp\u003e对于每个测试样例输入两个整数$$$n$$$ 和$$$k$$$ ($$$2 \\le n \\le 10^9$$$; $$$1 \\le k \\le 10^9$$$).\u003c/p\u003e"}},{"title":"Output","value":{"format":"HTML","content":"\u003cp\u003e对于每个测试样例,输出一个整数\u0026nbsp;— 第$$$k$$$个按升序排序的特殊数字\u003c/p\u003e\u003cp\u003e注意需要对$$$10^9+7$$$取模\u003c/p\u003e"}},{"title":"Example","value":{"format":"HTML","content":"\u003cdiv class\u003d\"sample-test\"\u003e\n \u003cdiv class\u003d\"input\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Input\n \u003c/div\u003e\n \u003cpre\u003e2\n3 4\n2 12\n\u003c/pre\u003e\n \u003c/div\u003e\n \u003cdiv class\u003d\"output\"\u003e\n \u003cdiv class\u003d\"title\"\u003e\n Output\n \u003c/div\u003e\n \u003cpre\u003e9\n12\n\u003c/pre\u003e\n \u003c/div\u003e\n\u003c/div\u003e"}},{"title":"Note","value":{"format":"HTML","content":"\u003cp\u003e当$$$n \u003d 3$$$的时候,这个序列为$$$[1,3,4,9...]$$$\u003c/p\u003e"}}]}