E869120 defined a sequence $a$ like this:


* $a_1=a_2=1$, $a_{k+2}=a_{k+1}+a_k \ (k \ge 1)$


He also defined sequences $d_1, d_2, d_3, \dots , d_n$, as the following recurrence relation :


* $d_{1, j} = a_j$
* $d_{i, j} = \sum_{k = 1}^j d_{i - 1, k} \ (i \ge 2)$


You are given integers $n$ and $m$. Please calculate the value of $d_{n, m}$.
Since the answer can be large number, print the answer modulo $998,244,353$.
Can you solve this problem???

Input

The input is given from standard input in the following format.



> $n \quad m$

Output

* Print $d_{n, m}$ modulo $998,244,353$.



Constraints

* $1 \le n \le 200,000$
* $1 \le m \le 10^{18}$



Subtasks

Subtask 1 [ $100$ points ]


* The testcase in this subtask satisfies $1 \le n, m \le 3,000$.

Subtask 2 [ $170$ points ]


* The testcase in this subtask satisfies $1 \le m \le 200,000$.

Subtask 3 [ $230$ points ]


* The testcase in this subtask satisfies $1 \le n \le 3$.

Subtask 4 [ $420$ points ]


* The testcase in this subtask satisfies $1 \le n \le 1000$.

Subtask 5 [ $480$ points ]


* There are no additional constraints.

Output

* Print $d_{n, m}$ modulo $998,244,353$.



Constraints

* $1 \le n \le 200,000$
* $1 \le m \le 10^{18}$



Subtasks

Subtask 1 [ $100$ points ]


* The testcase in this subtask satisfies $1 \le n, m \le 3,000$.

Subtask 2 [ $170$ points ]


* The testcase in this subtask satisfies $1 \le m \le 200,000$.

Subtask 3 [ $230$ points ]


* The testcase in this subtask satisfies $1 \le n \le 3$.

Subtask 4 [ $420$ points ]


* The testcase in this subtask satisfies $1 \le n \le 1000$.

Subtask 5 [ $480$ points ]


* There are no additional constraints.

Input

The input is given from standard input in the following format.



> $n \quad m$

Examples

Input

4 7


Output

176


Input

12 20


Output

174174144


Input

16 30


Output

102292850
#include <bits/stdc++.h>
using namespace std;

const int mod = 998244353;

int64_t mul(int64_t x, int64_t y) {
    return (x % mod) * (y % mod) % mod;
}

int fib(long long n, int64_t a = 0, int64_t b = 1, int64_t c = 1, int a0 = 0, int a1 = 1) {
    if (n == 0) return a0;
    int na0 = n & 1 ? (a * a0 + b * a1) % mod : a0;
    int na1 = n & 1 ? (b * a0 + c * a1) % mod : a1;
    return fib(n >> 1, (a * a + b * b) % mod, b * (a + c) % mod, (b * b + c * c) % mod, na0, na1);
}

int main() {
    int n;
    int64_t m;
    cin >> n >> m;
    vector<int> inv(1010101);
    inv[1] = 1;
    for (int i = 2; i < 1010101; i++) inv[i] = mul(inv[mod % i], mod - mod / i);
    int ans = fib(m + 2 * (n - 1));
    int C = 1;
    for (int i = 0; i <= n - 2; i++) {
        ans += mul(C, mod - fib(n * 2 - 2 - 2 * i));
        ans %= mod;
        C = mul(C, mul(m - 1 + i + 1, inv[i + 1]));
    }
    cout << ans << endl;
}
