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2025 Argentinian Programming Tournament (TAP)/B. Block sum array.cpp

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+/* Problem URL: https://codeforces.com/gym/106054/problem/B */
+
+#include <bits/stdc++.h>
+#include <ext/pb_ds/assoc_container.hpp>
+#include <ext/pb_ds/tree_policy.hpp>
+
+using namespace std;
+using namespace __gnu_pbds;
+
+template <class T, class comp = less<>>
+using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;
+
+#define V vector
+
+#define rmin(a, b) a = min(a, b)
+#define rmax(a, b) a = max(a, b)
+
+#define rep(i, lim) for (int i = 0; i < (lim); i++)
+#define nrep(i, s, lim) for (int i = s; i < (lim); i++)
+
+#define repv(i, v) for (auto &i : (v))
+#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
+#define sortv(v) sort(v.begin(), v.end())
+#define all(v) (v).begin(), (v).end()
+
+using vi = vector<int>;
+using vvi = vector<vi>;
+using vvvi = vector<vvi>;
+using vvvvi = vector<vvvi>;
+
+using ll = long long;
+
+using vl = vector<ll>;
+using vvl = vector<vl>;
+using vvvl = vector<vvl>;
+using vvvvl = vector<vvvl>;
+
+template<class v>
+auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
+    os << vec[0];
+    for (size_t i = 1; i < vec.size(); i++) {
+        os << ' ' << vec[i];
+    }
+    os << '\n';
+    return os;
+}
+
+template<class v>
+auto operator>>(istream &is, vector<v> &vec)->istream& {
+    for (auto &i : vec) {
+        is >> i;
+    }
+    return is;
+}
+
+template<class v>
+auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
+    for (auto &i : vec) {
+        os << i[0];
+        for (size_t j = 1; j < i.size(); j++) {
+            os << ' ' << i[j];
+        }
+        os << '\n';
+    }
+    return os;
+}
+
+template<class v>
+auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
+    for (auto &i : vec) {
+        for (auto &j : i) {
+            is >> j;
+        }
+    }
+    return is;
+}
+
+int main()
+{
+    ios::sync_with_stdio(false);
+    cin.tie(nullptr);
+
+    int n, k;
+    cin >> n >> k;
+
+    const ll mod = 998244353;
+
+    auto fpow = [&](ll a, ll p) {
+        ll ans = 1;
+
+        rep(i, 31) {
+            if ((p >> i) & 1) {
+                ans *= a;
+                ans %= mod;
+            }
+            
+            a *= a;
+            a %= mod;
+        }
+
+        return ans;
+    };
+
+    auto comb = [&](ll n, ll k) {
+        ll ans = 1;
+        ll div = 1;
+
+        rep(i, k) {
+            ans *= (n - i);
+            ans %= mod;
+
+            div *= (i + 1);
+            div %= mod;
+        }
+
+        return (ans * fpow(div, mod - 2)) % mod;
+    };
+
+    vl b(n - k + 1);
+    cin >> b;
+
+    ll ans = b[0];
+    
+    rep(i, k) {
+        ll m = 0;
+        ll tmp = 0;
+        for (int j = i; j + 1 < b.size(); j += k) {
+            m += b[j] - b[j + 1];
+            rmax(tmp, m);
+        }
+
+        ans -= tmp;
+    }
+
+    if (ans < 0) {
+        cout << "0\n";
+        return 0;
+    }
+
+    cout << comb(ans + k - 1, k - 1) << '\n';
+}