package yukicoder_3679; import java.io.ByteArrayInputStream; import java.io.IOException; import java.io.InputStream; import java.io.PrintWriter; import java.util.Arrays; import java.util.InputMismatchException; public class Main3 { InputStream is; PrintWriter out; String INPUT = ""; static final int MOD = 1_000_000_007; void solve() { int p = ni(), Q = ni(), max = 2; int[] q = new int[Q]; for (int i = 0;i < Q;++ i) { q[i] = ni(); max = Math.max(max, q[i]); } long[] fib = new long[max]; fib[1] = 1; for (int i = 2;i < fib.length;++ i) fib[i] = (p * fib[i - 1] + fib[i - 2]) % MOD; long[] conv = convolute(fib, fib, 3, MOD); for (int i : q) { System.out.println(conv[i - 2]); } } public static final int[] NTTPrimes = {1053818881, 1051721729, 1045430273, 1012924417, 1007681537, 1004535809, 998244353, 985661441, 976224257, 975175681}; public static final int[] NTTPrimitiveRoots = {7, 6, 3, 5, 3, 3, 3, 3, 3, 17}; // public static final int[] NTTPrimes = {1012924417, 1004535809, 998244353, 985661441, 975175681, 962592769, 950009857, 943718401, 935329793, 924844033}; // public static final int[] NTTPrimitiveRoots = {5, 3, 3, 3, 17, 7, 7, 7, 3, 5}; public static long[] convoluteSimply(long[] a, long[] b, int P, int g) { int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2); long[] fa = nttmb(a, m, false, P, g); long[] fb = a == b ? fa : nttmb(b, m, false, P, g); for (int i = 0; i < m; i++ ) { fa[i] = fa[i] * fb[i] % P; } return nttmb(fa, m, true, P, g); } public static long[] convolute(long[] a, long[] b) { int USE = 2; int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2); long[][] fs = new long[USE][]; for (int k = 0; k < USE; k++ ) { int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; long[] fa = nttmb(a, m, false, P, g); long[] fb = a == b ? fa : nttmb(b, m, false, P, g); for (int i = 0; i < m; i++ ) { fa[i] = fa[i] * fb[i] % P; } fs[k] = nttmb(fa, m, true, P, g); } int[] mods = Arrays.copyOf(NTTPrimes, USE); long[] gammas = garnerPrepare(mods); int[] buf = new int[USE]; for (int i = 0; i < fs[0].length; i++ ) { for (int j = 0; j < USE; j++ ) buf[j] = (int)fs[j][i]; long[] res = garnerBatch(buf, mods, gammas); long ret = 0; for (int j = res.length - 1; j >= 0; j-- ) ret = ret * mods[j] + res[j]; fs[0][i] = ret; } return fs[0]; } public static long[] convolute(long[] a, long[] b, int USE, int mod) { int m = Math.max(2, Integer.highestOneBit(Math.max(a.length, b.length) - 1) << 2); long[][] fs = new long[USE][]; for (int k = 0; k < USE; k++ ) { int P = NTTPrimes[k], g = NTTPrimitiveRoots[k]; long[] fa = nttmb(a, m, false, P, g); long[] fb = a == b ? fa : nttmb(b, m, false, P, g); for (int i = 0; i < m; i++ ) { fa[i] = fa[i] * fb[i] % P; } fs[k] = nttmb(fa, m, true, P, g); } int[] mods = Arrays.copyOf(NTTPrimes, USE); long[] gammas = garnerPrepare(mods); int[] buf = new int[USE]; for (int i = 0; i < fs[0].length; i++ ) { for (int j = 0; j < USE; j++ ) buf[j] = (int)fs[j][i]; long[] res = garnerBatch(buf, mods, gammas); long ret = 0; for (int j = res.length - 1; j >= 0; j-- ) ret = (ret * mods[j] + res[j]) % mod; fs[0][i] = ret; } return fs[0]; } // static int[] wws = new int[270000]; // outer faster // Modifed Montgomery + Barrett private static long[] nttmb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P) << 1; int H = Long.numberOfTrailingZeros(K) * 2; long M = K * K / P; int[] wws = new int[1 << h - 1]; long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P); long w = (1L << 32) % P; for (int k = 0; k < 1 << h - 1; k++ ) { wws[k] = (int)w; w = modh(w * dw, M, H, P); } long J = invl(P, 1L << 32); for (int i = 0; i < h; i++ ) { for (int j = 0; j < 1 << i; j++ ) { for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++ , s++ , t++ ) { long u = (dst[s] - dst[t] + 2 * P) * wws[k]; dst[s] += dst[t]; if (dst[s] >= 2 * P) dst[s] -= 2 * P; // long Q = (u&(1L<<32)-1)*J&(1L<<32)-1; long Q = (u << 32) * J >>> 32; dst[t] = (u >>> 32) - (Q * P >>> 32) + P; } } if (i < h - 1) { for (int k = 0; k < 1 << h - i - 2; k++ ) wws[k] = wws[k * 2]; } } for (int i = 0; i < n; i++ ) { if (dst[i] >= P) dst[i] -= P; } for (int i = 0; i < n; i++ ) { int rev = Integer.reverse(i) >>> -h; if (i < rev) { long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if (inverse) { long in = invl(n, P); for (int i = 0; i < n; i++ ) dst[i] = modh(dst[i] * in, M, H, P); } return dst; } // Modified Shoup + Barrett private static long[] nttsb(long[] src, int n, boolean inverse, int P, int g) { long[] dst = Arrays.copyOf(src, n); int h = Integer.numberOfTrailingZeros(n); long K = Integer.highestOneBit(P) << 1; int H = Long.numberOfTrailingZeros(K) * 2; long M = K * K / P; long dw = inverse ? pow(g, P - 1 - (P - 1) / n, P) : pow(g, (P - 1) / n, P); long[] wws = new long[1 << h - 1]; long[] ws = new long[1 << h - 1]; long w = 1; for (int k = 0; k < 1 << h - 1; k++ ) { wws[k] = (w << 32) / P; ws[k] = w; w = modh(w * dw, M, H, P); } for (int i = 0; i < h; i++ ) { for (int j = 0; j < 1 << i; j++ ) { for (int k = 0, s = j << h - i, t = s | 1 << h - i - 1; k < 1 << h - i - 1; k++ , s++ , t++ ) { long ndsts = dst[s] + dst[t]; if (ndsts >= 2 * P) ndsts -= 2 * P; long T = dst[s] - dst[t] + 2 * P; long Q = wws[k] * T >>> 32; dst[s] = ndsts; dst[t] = ws[k] * T - Q * P & (1L << 32) - 1; } } // dw = dw * dw % P; if (i < h - 1) { for (int k = 0; k < 1 << h - i - 2; k++ ) { wws[k] = wws[k * 2]; ws[k] = ws[k * 2]; } } } for (int i = 0; i < n; i++ ) { if (dst[i] >= P) dst[i] -= P; } for (int i = 0; i < n; i++ ) { int rev = Integer.reverse(i) >>> -h; if (i < rev) { long d = dst[i]; dst[i] = dst[rev]; dst[rev] = d; } } if (inverse) { long in = invl(n, P); for (int i = 0; i < n; i++ ) { dst[i] = modh(dst[i] * in, M, H, P); } } return dst; } static final long mask = (1L << 31) - 1; public static long modh(long a, long M, int h, int mod) { long r = a - ((M * (a & mask) >>> 31) + M * (a >>> 31) >>> h - 31) * mod; return r < mod ? r : r - mod; } private static long[] garnerPrepare(int[] m) { int n = m.length; assert n == m.length; if (n == 0) return new long[0]; long[] gamma = new long[n]; for (int k = 1; k < n; k++ ) { long prod = 1; for (int i = 0; i < k; i++ ) { prod = prod * m[i] % m[k]; } gamma[k] = invl(prod, m[k]); } return gamma; } private static long[] garnerBatch(int[] u, int[] m, long[] gamma) { int n = u.length; assert n == m.length; long[] v = new long[n]; v[0] = u[0]; for (int k = 1; k < n; k++ ) { long temp = v[k - 1]; for (int j = k - 2; j >= 0; j-- ) { temp = (temp * m[j] + v[j]) % m[k]; } v[k] = (u[k] - temp) * gamma[k] % m[k]; if (v[k] < 0) v[k] += m[k]; } return v; } public static long invl(long a, long mod) { long b = mod; long p = 1, q = 0; while (b > 0) { long c = a / b; long d; d = a; a = b; b = d % b; d = p; p = q; q = d - c * q; } return p < 0 ? p + mod : p; } public static long pow(long a, long n, long mod) { // a %= mod; long ret = 1; int x = 63 - Long.numberOfLeadingZeros(n); for (; x >= 0; x-- ) { ret = ret * ret % mod; if (n << 63 - x < 0) ret = ret * a % mod; } return ret; } void run() throws Exception { is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes()); out = new PrintWriter(System.out); long s = System.currentTimeMillis(); solve(); out.flush(); if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms"); // Thread t = new Thread(null, null, "~", Runtime.getRuntime().maxMemory()){ // @Override // public void run() { // long s = System.currentTimeMillis(); // solve(); // out.flush(); // if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms"); // } // }; // t.start(); // t.join(); } public static void main(String[] args) throws Exception { new Main3().run(); } private byte[] inbuf = new byte[1024]; public int lenbuf = 0, ptrbuf = 0; private int readByte() { if (lenbuf == -1) throw new InputMismatchException(); if (ptrbuf >= lenbuf) { ptrbuf = 0; try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); } if (lenbuf <= 0) return -1; } return inbuf[ptrbuf++ ]; } private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); } private int skip() { int b; while ((b = readByte()) != -1 && isSpaceChar(b)); return b; } private double nd() { return Double.parseDouble(ns()); } private char nc() { return (char)skip(); } private String ns() { int b = skip(); StringBuilder sb = new StringBuilder(); while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ') sb.appendCodePoint(b); b = readByte(); } return sb.toString(); } private char[] ns(int n) { char[] buf = new char[n]; int b = skip(), p = 0; while (p < n && !(isSpaceChar(b))) { buf[p++ ] = (char)b; b = readByte(); } return n == p ? buf : Arrays.copyOf(buf, p); } private int[] na(int n) { int[] a = new int[n]; for (int i = 0; i < n; i++ ) a[i] = ni(); return a; } private long[] nal(int n) { long[] a = new long[n]; for (int i = 0; i < n; i++ ) a[i] = nl(); return a; } private char[][] nm(int n, int m) { char[][] map = new char[n][]; for (int i = 0; i < n; i++ ) map[i] = ns(m); return map; } private int[][] nmi(int n, int m) { int[][] map = new int[n][]; for (int i = 0; i < n; i++ ) map[i] = na(m); return map; } private int ni() { return (int)nl(); } private long nl() { long num = 0; int b; boolean minus = false; while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')); if (b == '-') { minus = true; b = readByte(); } while (true) { if (b >= '0' && b <= '9') { num = num * 10 + (b - '0'); } else { return minus ? -num : num; } b = readByte(); } } private static void tr(Object... o) { System.out.println(Arrays.deepToString(o)); } }