add 24518.cpp

storage/zeta/cpp/24518.cpp

@@ -0,0 +1,91 @@
+#include <cmath>
+#include <iostream>
+#include <vector>
+
+#define let auto
+#define fn auto
+#define usize size_t
+
+using namespace std;
+
+const usize MOD = 1'000'000'007;
+
+fn fastio() {
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+}
+
+fn well_known_sum_draft(usize n, usize m) -> usize {
+    let res = (usize) 0;
+    for (usize i = 1; i <= n; i++) {
+        res += (n / i) * (i % m);
+        res %= MOD;
+    }
+    return res;
+}
+
+fn well_known_subarr_sum(usize d, usize lo, usize hi /* exclusive */, usize m) -> usize {
+    let res = (usize) 0;
+
+    let lo_margin = lo % m;
+    let hi_margin = hi % m;
+    if (lo / m == hi / m) {
+        res += ((hi_margin * (hi_margin - 1) / 2) - (lo_margin * (lo_margin - 1) / 2)) * d;
+        res %= MOD;
+        return res;
+    }
+
+    res += (hi_margin * (hi_margin - 1) / 2) * d;
+    res %= MOD;
+
+    res += (m * (m - 1) / 2 - lo_margin * (lo_margin - 1) / 2) * d;
+    res %= MOD;
+
+    let d_cycle = (d * (m * (m - 1) / 2) % MOD) % MOD;
+    let cycle_cnt = (hi - lo - (hi_margin + m - lo_margin)) / m;
+    res += cycle_cnt * d_cycle;
+    res %= MOD;
+    return res;
+}
+
+fn well_known_sum(usize n, usize m) -> usize {
+    let res = (usize) 0;
+    let steps = vector<usize>();
+    steps.push_back(n + 1);
+    for (usize i = 2; i <= (usize) pow(n, 0.5) + 1; i++) {
+        steps.push_back(n / i + 1);
+    }
+
+    for (usize i = 1; i < (usize) pow(n, 0.5); i++) {
+        res += (n / i) * (i % m);
+        res %= MOD;
+    }
+
+    let step_size = steps.size();
+    for (usize i = 0; i < step_size - 1; i++) {
+        let temp = well_known_subarr_sum(i + 1, steps[i + 1], steps[i], m);
+        res += temp;
+        res %= MOD;
+    }
+
+    return res;
+}
+
+fn main() -> int {
+    fastio();
+    usize n;
+    usize m;
+
+    cin >> n;
+    cin >> m;
+
+    if (n <= 10) {
+        cout << well_known_sum_draft(n, m) << endl;
+    } else if (m == 1) {
+        cout << 0 << endl;
+    } else {
+        cout << well_known_sum_draft(n, m) << endl;
+        cout << well_known_sum(n, m) << endl;
+    }
+    return 0;
+}