#include #include #include #include #include #include #include #include #include #include #include #include #include #include #define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl; #define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } using namespace std; typedef long long ll; template vector> vec2d(int n, int m, T v){ return vector>(n, vector(m, v)); } template vector>> vec3d(int n, int m, int k, T v){ return vector>>(n, vector>(m, vector(k, v))); } template void print_vector(vector v, char delimiter=' '){ if(v.empty()) { cout << endl; return; } for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter; cout << v.back() << endl; } const ll MOD = 998244353; using mint = atcoder::modint998244353; ostream& operator<<(ostream& os, const mint& m){ os << m.val(); return os; } mint test(int n, int m){ auto dp = vec2d(n+1, m, mint(0)); dp[0][0] = 1; for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ for(int k = 0; k < m-1; k++){ dp[i+1][(j+k)%m] += dp[i][j]; } } print_vector(dp[i+1]); } } int main(){ ios::sync_with_stdio(false); cin.tie(0); cout << setprecision(10) << fixed; int n, m; cin >> n >> m; // test(n, m); vector a(n); for(int i = 0; i < n; i++) cin >> a[i]; int sum = 0; for(int i = 0; i < n; i++){ if(i%2 == 0) sum += a[i]; else sum -= a[i]; sum += m; sum %= m; } if(sum != 0){ cout << -1 << endl; return 0; } mint ans = 1; int x = 0; for(int i = 0; i < n; i++){ // ここで初めて小さくなるパターン if(a[i] > 0){ int rem = n-i-1; if(rem == 0){ continue; } mint tmp; mint offset; if(rem%2 == 0){ mint ave = (mint(m-1).pow(rem)-1)/(m); tmp = ave*a[i]; offset = 1; }else{ mint ave = (mint(m-1).pow(rem)+1)/(m); tmp = ave*a[i]; offset = -1; } int l = 0, r = 0; if(i%2 == 1){ l = x-(a[i]-1); r = x; }else{ l = x; r = x+a[i]-1; } if(i%2 == 0){ l -= (rem/2)*2; r -= (rem/2)*2; }else{ l -= ((rem+1)/2)*2; r -= ((rem+1)/2)*2; } l %= m; r %= m; l = (l+m)%m; r = (r+m)%m; int small_idx = (m-rem)%m; small_idx = (small_idx+m)%m; // cout << l << ' ' << r << ' ' << small_idx << endl; if(r >= l){ if(l <= small_idx && small_idx <= r) { tmp+=offset; } }else{ if(small_idx >= l || small_idx <= r) { tmp+=offset; } } ans += tmp; } if(i%2 == 0) x += a[i]; else x += m-a[i]; x %= m; } cout << ans << endl; }