#include <bits/stdc++.h> using namespace std; const int MOD = 998244353; int add(int x, int y) { x += y; if (x >= MOD) { x -= MOD; } return x; } int expo(int a, long long n, int mod) { int ans = 1; while (n) { if (n & 1LL) { ans = ((long long) ans * a) % mod; } n >>= 1; a = ((long long) a * a) % mod; } return ans; } int revMod(int a, int mod) { return expo(a, mod - 2, mod); } pair <int,int> join(int x, bool bx, int y, bool by) { return { x + y - (bx && by), bx && by ? 0 : bx }; } vector <int> countUnrooted(int n, int c) { vector <vector<int>> dpRooted(n + 1, vector <int> (2, 0)); dpRooted[1][1] = c; auto getCoefs = [&](int i, int v) { vector <int> coefs = {1}; int coef = 1; for (int j = 1; (j - 1) * i <= n; j++) { coef = ((long long) coef * (v - 1 + j)) % MOD; coef = ((long long) coef * revMod(j, MOD)) % MOD; coefs.push_back(coef); } return coefs; }; for (int i = 1; i <= n; i++) { int v0 = dpRooted[i][0], v1 = dpRooted[i][1]; int v2 = (v0 + (long long) v1 * c) % MOD; auto coefsFirst = getCoefs(i, v1); auto coefsSecond = getCoefs(i, v2); for (int j = n; j >= i + 1; j--) for (int m = 1; m * i <= j; m++) { int sum = add(dpRooted[j - m * i][0], dpRooted[j - m * i + 1][1]); dpRooted[j][0] = (dpRooted[j][0] + (long long) coefsFirst[m] * sum) % MOD; } dpRooted[i][0] = v2; for (int j = n; j >= i + 1; j--) for (int m = 1; m * i < j; m++) { for (int b = 0; b <= 1; b++) { dpRooted[j][b] = (dpRooted[j][b] + (long long) coefsSecond[m] * dpRooted[j - m * i][b]) % MOD; } } } vector <vector<int>> dpUnrooted = dpRooted; for (int i = 1; i <= n; i++) for (int bi = 0; bi <= 1; bi++) { for (int j = i; j <= n; j++) for (int bj = 0; bj <= 1; bj++) { if (i == j && bi > bj) { continue; } int numWays; if (i != j || bi != bj) { numWays = ((long long) dpRooted[i][bi] * dpRooted[j][bj]) % MOD; } else { numWays = ((long long) dpRooted[i][bi] * (dpRooted[i][bi] - 1) / 2) % MOD; } auto [k, bk] = join(i, bi, j, bj); if (k <= n) { dpUnrooted[k][bk] = add(dpUnrooted[k][bk], MOD - numWays); } } } vector <int> cntUnrooted(n + 1, 0); for (int i = 1; i <= n; i++) for (int bi = 0; bi <= 1; bi++) { cntUnrooted[i] = add(cntUnrooted[i], dpUnrooted[i][bi]); } return cntUnrooted; } int solve(int l, int r, int c) { auto cntUnrooted = countUnrooted(r, c); int ans = 0; for (int i = l; i <= r; i++) { ans = add(ans, cntUnrooted[i]); } return ans; } int main() { ios_base::sync_with_stdio(false); int l, r, c; cin >> l >> r >> c; cout << solve(l, r, c); return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 | #include <bits/stdc++.h> using namespace std; const int MOD = 998244353; int add(int x, int y) { x += y; if (x >= MOD) { x -= MOD; } return x; } int expo(int a, long long n, int mod) { int ans = 1; while (n) { if (n & 1LL) { ans = ((long long) ans * a) % mod; } n >>= 1; a = ((long long) a * a) % mod; } return ans; } int revMod(int a, int mod) { return expo(a, mod - 2, mod); } pair <int,int> join(int x, bool bx, int y, bool by) { return { x + y - (bx && by), bx && by ? 0 : bx }; } vector <int> countUnrooted(int n, int c) { vector <vector<int>> dpRooted(n + 1, vector <int> (2, 0)); dpRooted[1][1] = c; auto getCoefs = [&](int i, int v) { vector <int> coefs = {1}; int coef = 1; for (int j = 1; (j - 1) * i <= n; j++) { coef = ((long long) coef * (v - 1 + j)) % MOD; coef = ((long long) coef * revMod(j, MOD)) % MOD; coefs.push_back(coef); } return coefs; }; for (int i = 1; i <= n; i++) { int v0 = dpRooted[i][0], v1 = dpRooted[i][1]; int v2 = (v0 + (long long) v1 * c) % MOD; auto coefsFirst = getCoefs(i, v1); auto coefsSecond = getCoefs(i, v2); for (int j = n; j >= i + 1; j--) for (int m = 1; m * i <= j; m++) { int sum = add(dpRooted[j - m * i][0], dpRooted[j - m * i + 1][1]); dpRooted[j][0] = (dpRooted[j][0] + (long long) coefsFirst[m] * sum) % MOD; } dpRooted[i][0] = v2; for (int j = n; j >= i + 1; j--) for (int m = 1; m * i < j; m++) { for (int b = 0; b <= 1; b++) { dpRooted[j][b] = (dpRooted[j][b] + (long long) coefsSecond[m] * dpRooted[j - m * i][b]) % MOD; } } } vector <vector<int>> dpUnrooted = dpRooted; for (int i = 1; i <= n; i++) for (int bi = 0; bi <= 1; bi++) { for (int j = i; j <= n; j++) for (int bj = 0; bj <= 1; bj++) { if (i == j && bi > bj) { continue; } int numWays; if (i != j || bi != bj) { numWays = ((long long) dpRooted[i][bi] * dpRooted[j][bj]) % MOD; } else { numWays = ((long long) dpRooted[i][bi] * (dpRooted[i][bi] - 1) / 2) % MOD; } auto [k, bk] = join(i, bi, j, bj); if (k <= n) { dpUnrooted[k][bk] = add(dpUnrooted[k][bk], MOD - numWays); } } } vector <int> cntUnrooted(n + 1, 0); for (int i = 1; i <= n; i++) for (int bi = 0; bi <= 1; bi++) { cntUnrooted[i] = add(cntUnrooted[i], dpUnrooted[i][bi]); } return cntUnrooted; } int solve(int l, int r, int c) { auto cntUnrooted = countUnrooted(r, c); int ans = 0; for (int i = l; i <= r; i++) { ans = add(ans, cntUnrooted[i]); } return ans; } int main() { ios_base::sync_with_stdio(false); int l, r, c; cin >> l >> r >> c; cout << solve(l, r, c); return 0; } |