#include "bits/stdc++.h" #define MOD 1000000007 #define rep(i, n) for(ll i=0; i < (n); i++) #define rrep(i, n) for(ll i=(n)-1; i >=0; i--) #define ALL(v) v.begin(),v.end() #define rALL(v) v.rbegin(),v.rend() #define FOR(i, j, k) for(ll i=j;i llvec; typedef vector dvec; typedef pair P; typedef long double ld; struct edge{ll x, c;}; ll mod(ll a, ll mod){ ll res = a%mod; if(res<0)res=res + mod; return res; } ll modpow(ll a, ll n, ll mod){ ll res=1; while(n>0){ if(n&1) res=res*a%mod; a=a*a%mod; n>>=1; } return res; } ll modinv(ll a, ll mod){ ll b=mod, u=1, v=0; while(b){ ll t=a/b; a-=t*b; swap(a, b); u-=t*v; swap(u, v); } u%=mod; if(u<0)u+=mod; return u; } ll gcd(ll a, ll b){ ll r = a%b; if(r==0) return b; else return gcd(b, a%b); } // @param b 1 // @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g std::pair inv_gcd(long long a, long long b) { a = mod(a, b); if (a == 0) return {b, 0}; // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if (m0 < 0) m0 += b / s; return {s, m0}; } // (rem, mod) std::pair crt(const std::vector& r, const std::vector& m) { assert(r.size() == m.size()); int n = int(r.size()); // Contracts: 0 <= r0 < m0 long long r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); long long r1 = mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1) // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1)); // r2 % m0 = r0 // r2 % m1 = r1 // -> (r0 + x*m0) % m1 = r1 // -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1) // -> x = (r1 - r0) / g * inv(u0) (mod u1) // im = inv(u0) (mod u1) (0 <= im < u1) long long g, im; std::tie(g, im) = inv_gcd(m0, m1); long long u1 = (m1 / g); // |r1 - r0| < (m0 + m1) <= lcm(m0, m1) if ((r1 - r0) % g) return {0, 0}; // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1) long long x = (r1 - r0) / g % u1 * im % u1; // |r0| + |m0 * x| // < m0 + m0 * (u1 - 1) // = m0 + m0 * m1 / g - m0 // = lcm(m0, m1) r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if (r0 < 0) r0 += m0; } return {r0, m0}; } bool is_prime(ll n){ ll i = 2; if(n==1)return false; if(n==2)return true; bool res = true; while(i*i n){ return 0; }else{ return mod(mod(frac[n]*ifrac[n-k], MOD)*ifrac[k], MOD); } } /************************************** ** A main function starts from here ** ***************************************/ int main(){ ll N, K; cin >> N >> K; ll ans = 0; gen(); llvec frac2(N+1, 0); frac2[0] = 1; rep(i, N){ frac2[i+1] = mod(frac2[i]*(K+1+i), MOD); } rep(i, N){ ll a; cin >> a; ll tmp = a; tmp = mod(tmp*frac2[i], MOD); tmp = mod(tmp*ifrac[i], MOD); tmp = mod(tmp*frac2[N-i-1], MOD); tmp = mod(tmp*ifrac[N-i-1], MOD); ans = mod(ans + tmp, MOD); } cout << ans << endl; return 0; }