{"trustable":true,"prependHtml":"\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 async src\u003d\"https://mathjax.codeforces.org/MathJax.js?config\u003dTeX-AMS-MML_HTMLorMML\" type\u003d\"text/javascript\"\u003e\u003c/script\u003e","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv class\u003d\"panel_content\"\u003ePatrick Star found a kind of magical matrixs, he named them $HMBB$ !!!\u003cbr\u003e\u003cbr\u003eWe use $p$ to express the $c$-th prime number. \u003cbr\u003e\u003cbr\u003eThe size of $HMBB_i$ is $p^i * p^i$ ! \u003cbr\u003e\u003cbr\u003eWhat is more surprising is that :\u003cbr\u003e\u003cbr\u003e1. For any $n$, the element on the i-th row j-th column $HMBB_n[i][j]$ \u003d $(C(i, j)\\ mod\\ p) \u0026gt; 0)$ ? $1$ : $0$. \u003cbr\u003e\u003cbr\u003e2. Where $C(i, j)$ is count of method to choose $j$ balls (unordered) from $i$ balls which are pairwise distinct.\u003cbr\u003e\u003cbr\u003e3. Note that rows and columns both count from zero.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003ePatrick Star defined $F[n][k]$ the sum of all elements of $(HMBB_n)^k$, $F[n][k] \u003d \\sum_{i \u003d 0}^{p^n-1}\\sum_{j\u003d0}^{p^n-1}HMBB_n^k[i][j]$\u003cbr\u003e\u003cbr\u003eNow Patrick wants to know $(\\sum_{i\u003d1}^n\\sum_{j\u003d1}^kF[i][j])\\ mod\\ (10^9 + 7)$ !\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"The first line contain a integer $T$ (no morn than 10), the following is $T$ test case, for each test case :\u003cbr\u003e\u003cbr\u003eEach line contains contains three integer c, n, k ($0 \u0026lt; n \\le 10^9$, $0 \u0026lt; c, k \\le 10^5$). Separated by an white space."}},{"title":"Output","value":{"format":"HTML","content":"For each test case output one line denotes the answer that Patrick Star wants to know."}},{"title":"Sample","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\u003e1\r\n1 1 1\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e3\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}