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
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
#pragma GCC OPTIMIZE("O3,unroll-loops")
#include <bits/stdc++.h>

using namespace std;

const int N = 5'007;
const int MOD = 998'244'353;

int dp[N][2];
int knewt[N][2];

int mem_dp[N][3][2];
int help_dp[2][N][2];

int coef[N][2];
int dp_coef[2][N][N][2];

int rev_nr[N];
int rev_sil[N];

int fast(int a, int b)
{
    int ret = 1;
    while (b) {
        if (b & 1) {
            ret = 1LL * ret * a % MOD;
        }

        b >>= 1;
        a = 1LL * a * a % MOD;
    }

    return ret;
}

int newton(int a, int b) {
    int ret = 1;
    for (int i = 0; i < b; ++i) {
        ret = 1LL * ret * (a - i) % MOD;
        ret = 1LL * ret * rev_nr[i + 1] % MOD;
    }
    
    return ret;
}

void get_coefs(int n, int c)
{
    dp_coef[(n + 1) & 1][0][0][0] = 1;
    dp_coef[(n + 1) & 1][0][0][1] = 1;

    for (int i = n; i >= 1; --i) {
        int id = i & 1;
        int max_take = n / i, prev_max = n / (i + 1);

        dp_coef[id][0][0][0] = dp_coef[id][0][0][1] = 1;
        for (int j = 1; j <= max_take && j <= c; ++j) {
            for (int s = 1; s <= n; ++s) {
                for (int t = 0; t < 2; ++t) {
                    int cur = 1;
                    __int128_t tmp = j <= prev_max ? dp_coef[id ^ 1][j][s][t] : 0;

                    for (int k = 1; k * i <= s && k <= j; ++k) {
                        cur = 1LL * cur * rev_nr[k] % MOD * knewt[i][t] % MOD;
                        if (j - k <= prev_max) {
                            tmp += 1LL * cur * dp_coef[id ^ 1][j - k][s - k * i][t];
                        }
                    }

                    dp_coef[id][j][s][t] = tmp % MOD;
                }
            }
        }
    }

    for (int i = 1; i <= n; ++i) {
        for (int t = 0; t < 2; ++t) {
            coef[i][t] = 0;

            int cur = 1;
            for (int j = 1; j <= i && j <= c; ++j) {
                cur = 1LL * cur * (c - j + 1) % MOD;
                coef[i][t] = (coef[i][t] + 1LL * cur * dp_coef[1][j][i][t]) % MOD;
            }
        }
    }
}

void precalc(int n, int c)
{
    dp[1][0] = c;
    dp[1][1] = 1;

    help_dp[0][0][0] = 1;
    mem_dp[0][0][0] = 1;
    
    for (int i = 1; i < n; ++i) {
        int id = i & 1;
        help_dp[id][0][0] = 1;

        int max_k = n / i;
        knewt[0][0] = knewt[0][1] = 1;

        for (int k = 1; k <= max_k; ++k) {
            knewt[k][0] = 1LL * knewt[k - 1][0] * (dp[i][0] + k - 1) % MOD * rev_nr[k] % MOD;
            knewt[k][1] = 1LL * knewt[k - 1][1] * (dp[i][0] + dp[i][1] + k - 1) % MOD * rev_nr[k] % MOD;
        }

        get_coefs(max_k, c);
        for (int j = 1; j <= n; ++j) {
            help_dp[id][j][0] = help_dp[id ^ 1][j][0];
            help_dp[id][j][1] = help_dp[id ^ 1][j][1];

            for (int k = 1; k * i <= j; ++k) {
                int val0 = coef[k][0];
                help_dp[id][j][0] = (help_dp[id][j][0] + 1LL * help_dp[id ^ 1][j - k * i][0] * val0) % MOD;

                int val01 = coef[k][1];
                help_dp[id][j][1] = (help_dp[id][j][1] + 1LL * help_dp[id ^ 1][j - k * i][1] * val01) % MOD;
                help_dp[id][j][1] = (help_dp[id][j][1] + 1LL * help_dp[id ^ 1][j - k * i][0] * (val01 + MOD - val0)) % MOD;
            }
        }

        if (i + i <= n) {
            for (int off = 0; off < 3; ++off) {
                for (int t = 0; t < 2; ++t) {
                    mem_dp[i][off][t] = help_dp[id][i + i + off][t];
                }
            }
        }

        dp[i + 1][1] = help_dp[id][i][0];
        dp[i + 1][0] = (help_dp[id][i + 1][1] + 1LL * c * dp[i + 1][1]) % MOD;
    }
}

inline int square(const int x) {
    return 1LL * x * x % MOD;
}

int calc(int n, int c)
{
    int mid = (n - 1) / 2;
    int ans = 1LL * c * (mem_dp[mid][n - 1 - 2 * mid][0] + mem_dp[mid][n - 2 * mid][1]) % MOD;

    if (n & 1) {
        mid = (n + 1) / 2;
        ans = (ans + 1LL * c * newton(dp[mid][1] + 1, 2)) % MOD;
        ans = (ans + 1LL * newton(c, 2) * square(dp[mid][1])) % MOD;
    } else {
        int dp_00 = dp[n / 2][0] + MOD - 1LL * c * dp[n / 2][1] % MOD;
        ans = (ans + 1LL * c * newton(dp_00 + 1, 2)) % MOD;
        ans = (ans + 1LL * newton(c, 2) * square(dp_00)) % MOD;

        ans = (ans + 1LL * square(c) * dp_00 % MOD * dp[n / 2][1]) % MOD;
        ans = (ans + 1LL * c * square(c) % MOD * dp_00 % MOD * dp[n / 2][1]) % MOD;

        ans = (ans + 1LL * square(c) * newton(dp[n / 2][1] + 1, 2)) % MOD;
        ans = (ans + 1LL * newton(c, 2) * c % MOD * square(dp[n / 2][1])) % MOD;

        int dp_11 = 1LL * c * dp[n / 2][1] % MOD;
        ans = (ans + 1LL * c * newton(dp_11 + 1, 2)) % MOD;
        ans = (ans + 1LL * newton(c, 2) * square(dp_11)) % MOD;

        int dp_10 = dp[n / 2 + 1][1] + MOD - 1LL * dp[n / 2][0] * c % MOD;
        ans = (ans + 1LL * square(c) * dp[n / 2][1] % MOD * dp_10) % MOD;
    }

    return ans;
}

int main()
{
    int cur = rev_nr[0] = 1;
    for (int i = 1; i < N; ++i) {
        rev_nr[i] = cur;
        cur = 1LL * cur * i % MOD;
    }

    rev_sil[N - 1] = fast(cur, MOD - 2);
    for (int i = N - 1; i >= 1; --i) {
        rev_sil[i - 1] = 1LL * rev_sil[i] * i % MOD;
        rev_nr[i] = 1LL * rev_nr[i] * rev_sil[i] % MOD;
    }

    int l, r, c;
    scanf("%d %d %d", &l, &r, &c);
    precalc(r, c);

    int s = 0;
    for (int i = l; i <= r; ++i) {
        int v = calc(i, c);
        s = (s + v) % MOD;
    }

    printf("%d\n", s);
    return 0;
}