#include using namespace std; #define repu(i, begin, end) for (__typeof(begin) i = (begin) - ((begin) > (end)); i != (end) - ((begin) > (end)); i += 1 - 2 * ((begin) > (end))) #define repe(i, begin, end) for (__typeof(begin) i = (begin); i != (end) + 1 - 2 * ((begin) > (end)); i += 1 - 2 * ((begin) > (end))) #define mem(a, x) memset(a, x, sizeof(a)) #define all(a) a.begin(), a.end() #define count_bits(x) __builtin_popcount(x) #define count_bitsll(x) __builtin_popcountll(x) #define least_bits(x) __builtin_ffs(x) #define least_bitsll(x) __builtin_ffsll(x) #define most_bits(x) 32 - __builtin_clz(x) #define most_bitsll(x) 64 - __builtin_clz(x) vector split(const string &s, char c) { vector v; stringstream ss(s); string x; while (getline(ss, x, c)) v.push_back(x); return v; } #define error(args...) { vector _v = split(#args, ','); err(_v.begin(), args); } void err(vector::iterator it) {} template void err(vector::iterator it, T a, Args... args) { cerr << it -> substr((*it)[0] == ' ', it -> length()) << " = " << a << '\n'; err(++it, args...); } typedef long long ll; const int MOD = 1000000007; template inline T tmin(T a, T b) {return (a < b) ? a : b;} template inline T tmax(T a, T b) {return (a > b) ? a : b;} template inline void amax(T &a, T b) {if (b > a) a = b;} template inline void amin(T &a, T b) {if (b < a) a = b;} template inline T tabs(T a) {return (a > 0) ? a : -a;} template T gcd(T a, T b) {while (b != 0) {T c = a; a = b; b = c % b;} return a;} const int N = 10005; int n, a[N]; ll k; typedef vector vl; typedef vector Mat; void unit(Mat &data) { int sz = data.size(); repu(i, 0, sz) data[i][i] = 1; } Mat mul(Mat x, Mat y) { int sz = x.size(); Mat ans(sz, vl(sz, 0)); repu(i, 0, sz) repu(j, 0, sz) repu(l, 0, sz) { ans[i][j] = (ans[i][j] + x[i][l] * y[l][j]) % MOD; } return ans; } Mat pow(Mat x, ll _n) { int sz = x.size(); Mat ans(sz, vl(sz, 0)); unit(ans); while (_n) { if (_n & 1) ans = mul(ans, x); x = mul(x, x); _n >>= 1; } return ans; } void solve_small() { vector f(k); ll s = 0, tot = 0; repu(i, 0, n) { f[i] = a[i]; tot += a[i]; } s = tot; repu(i, n, k) { f[i] = tot; tot = (tot + f[i] - f[i - n]) % MOD; if (tot < 0) tot += MOD; s = (s + f[i]) % MOD; } printf("%lld %lld\n", f[k - 1], s); } void solve_large() { Mat base(n + 1, vl(n + 1, 0)); repu(i, 0, n) base[0][i] = 1; repu(i, 1, n) base[i][i - 1] = 1; repu(i, 0, n + 1) base[n][i] = 1; ll tot = 0; repu(i, 0, n) tot += a[i]; Mat ret = pow(base, k - n); ll fk = 0, s = 0; repu(i, 0, n) { fk += ret[0][i] * a[n - 1 - i]; s += ret[n][i] * a[n - 1 - i]; } fk += ret[0][n] * tot; fk %= MOD; s += ret[n][n] * tot; s %= MOD; printf("%lld %lld\n", fk, s); } int main(int argc, char *argv[]) { ios_base::sync_with_stdio(false); cin >> n >> k; repu(i, 0, n) cin >> a[i]; if (n <= 10000 && k <= 1000000) solve_small(); else solve_large(); return 0; }