{"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\"\u003eMr. Furion is a math teacher. His students are very lazy and they do not like to do their homework. One day, Mr. Furion decides to give them a special problem in order to see whether his students are talents in math or they are just too lazy to do their homework. The problem is:\u003cbr\u003e\u003cbr\u003e\u003cbr\u003eGiven an integer k, n integers m\u003csub\u003e1\u003c/sub\u003e,m\u003csub\u003e2\u003c/sub\u003e…m\u003csub\u003en\u003c/sub\u003e, and a formula below: \u003cbr\u003e\u003cbr\u003eX\u003csub\u003e1\u003c/sub\u003e xor X\u003csub\u003e2\u003c/sub\u003e xor X\u003csub\u003e3\u003c/sub\u003e… xor X\u003csub\u003en\u003c/sub\u003e \u003d k \u003cbr\u003e\u003cbr\u003ePlease figure out that how many integral solutions of the formula can satisfy:\u003cbr\u003e\u003cbr\u003e0\u0026lt;\u003dX\u003csub\u003ei\u003c/sub\u003e\u0026lt;\u003dm\u003csub\u003ei\u003c/sub\u003e (i\u003d1…n)\u003c/div\u003e"}},{"title":"Input","value":{"format":"HTML","content":"There are at most 100 test cases.\u003cbr\u003e\u003cbr\u003eThe first line of each test case contains two integers n and k. The second line of each test contains n integers: m\u003csub\u003e1\u003c/sub\u003e,m\u003csub\u003e2\u003c/sub\u003e…m\u003csub\u003en\u003c/sub\u003e. The meaning of n,k, m\u003csub\u003e1\u003c/sub\u003e,m\u003csub\u003e2\u003c/sub\u003e…m\u003csub\u003en\u003c/sub\u003e are described above. (1\u0026lt;\u003dn\u0026lt;\u003d50,0\u0026lt;\u003dk,m\u003csub\u003e1\u003c/sub\u003e,m\u003csub\u003e2\u003c/sub\u003e…m\u003csub\u003en\u003c/sub\u003e\u0026lt;\u003d2\u003csup\u003e^31\u003c/sup\u003e-1 )\u003cbr\u003e\u003cbr\u003eThe input is ended by “0 0”."}},{"title":"Output","value":{"format":"HTML","content":"You should output a integer for each test case, which is the number of solutions. As the number might be very large, you should only output the number modulo 1000000003."}},{"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\u003e11 2047\r\n1024 512 256 128 64 32 16 8 4 2 1\r\n10 2047\r\n1024 512 256 128 64 32 16 8 4 2 \r\n0 0\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e1\r\n0\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}