\u8bbe \u62c9\u683c\u6717\u65e5\u63d2\u503c\u6c42\u89e3\u3002\u3002 [toc] XOR Sum \u8bbef(i, k) = 1 \\bigoplus 2 \\bigoplus 3 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[60],"tags":[],"_links":{"self":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/855"}],"collection":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/comments?post=855"}],"version-history":[{"count":14,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/855\/revisions"}],"predecessor-version":[{"id":860,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/posts\/855\/revisions\/860"}],"wp:attachment":[{"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/media?parent=855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/categories?post=855"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.zyhcoding.club\/index.php\/wp-json\/wp\/v2\/tags?post=855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}f(i, k) = 1 \\bigoplus 2 \\bigoplus 3 ...\\bigoplus i^k<\/code>
\n\u7ed9\u5b9a\u4e09\u4e2a\u6574\u6570t, x, y, \u6c42\u4e0b\u9762\u516c\u5f0f\u5bf91e9+7\u53d6\u6a21\u7684\u503c\u3002<\/p>\n\\sum_{k=1}^{t} \\sum_{i=x}^{y} f(i, k)<\/code><\/p>\n
\n\u9996\u5148\u5206\u6790f\u51fd\u6570\uff0c\u53d1\u73b0\uff1a
\n![\"\"](\"http:\/\/www.zyhcoding.club:80\/wp-content\/uploads\/2020\/10\/\u516c\u5f0f.png\")
\n\u53ef\u4ee5\u636e\u6b64\u6765\u63a8\u516c\u5f0f
\n\\sum_{k=1}^{t} \\sum_{i=x}^{y} f(i, k) = \\sum_{k=1}^{t} \\sum_{i=1}^{y} f(i, k) - \\sum_{k=1}^{t} \\sum_{i=1}^{x-1} f(i, k)<\/code>
\n\\sum_{k=1}^{t} \\sum_{i=1}^{x} f(i, k) = \\sum_{k=1}^{t} \\sum_{i=1}^{x} i^k[i^k\\%2==0] + \\sum_{k=1}^{t} \\sum_{i=1}^{x} [i^k\\%4 == 1 or 2]<\/code>
\n\u5bf9\u4e8e\u4e0a\u5f0f<\/p>\n#include <bits\/stdc++.h>\n\nusing namespace std;\ntypedef long long ll;\nconst ll maxn = 1e5+5, mod = 1e9+7;\nll t, a, b;\nll pre[maxn], suf[maxn], fac[maxn], y[maxn];\nll pow_mod(ll a, ll b){\n a %= mod, b %= mod-1;\n if (!a) return 0;\n ll ans = 1;\n while (b){\n if (b&1) ans = ans*a%mod;\n b >>= 1;\n a = a*a%mod;\n }\n return ans;\n}\nll inv(ll a){\n a = (a%mod+mod)%mod;\n return pow_mod(a, mod-2);\n}\nll Lagrange(ll x){\n ll ans = t*(x\/4%mod+((x%4)?1:0)) + x\/4%mod + (x%4>=2) + t\/2*(x\/4%mod+(x%4>=3));\n pre[0] = suf[t+2+1] = 1;\n x \/= 2; x %= mod;\n for (int i=1; i<=t+2; i++) pre[i] = pre[i-1]*(x-i)%mod;\n for (int i=t+2; i>=1; i--) suf[i] = suf[i+1]*(x-i)%mod;\n for (int i=1; i<=t+2; i++){\n int flag = 1;\n if ((t+2-i)&1) flag = -1;\n ans = (ans + y[i]*pre[i-1]%mod*suf[i+1]%mod*inv(fac[i-1])%mod*inv(fac[t+2-i])%mod*flag)%mod;\n }\n return ans;\n}\n\nint main(){\n ll ans;\n cin >> t >> a >> b;\n fac[0] = 1;\n for (int i=1; i<=t+3; i++) fac[i] = fac[i-1]*i%mod;\n for (ll i=1; i<=t+2; i++) y[i] = (y[i-1]+2*i*(pow_mod(2*i, t)-1)%mod*inv(2*i-1)%mod)%mod;\n ans = Lagrange(b) - Lagrange(a-1);\n ans = (ans%mod+mod)%mod;\n cout << ans;\n return 0;\n}<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"