package contest180727; 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 C { InputStream is; PrintWriter out; String INPUT = ""; void solve() { long n = nl(); int m = ni(); int[][] M = { {1, 1}, {1, 0} }; M = pow(M, m); int[][] U = { {M[0][0], M[0][1], 0}, {M[1][0], M[1][1], 0}, {0, 1, 1} }; out.println(pow(U, new int[]{1, 0, 0}, n+1)[2]); } ///////// begin public static final int mod = 1000000007; public static final long m2 = (long)mod*mod; public static final long BIG = 8L*m2; // A^e*v public static int[] pow(int[][] A, int[] v, long e) { for(int i = 0;i < v.length;i++){ if(v[i] >= mod)v[i] %= mod; } int[][] MUL = A; for(;e > 0;e>>>=1) { if((e&1)==1)v = mul(MUL, v); MUL = p2(MUL); } return v; } // int matrix*int vector public static int[] mul(int[][] A, int[] v) { int m = A.length; int n = v.length; int[] w = new int[m]; for(int i = 0;i < m;i++){ long sum = 0; for(int k = 0;k < n;k++){ sum += (long)A[i][k] * v[k]; if(sum >= BIG)sum -= BIG; } w[i] = (int)(sum % mod); } return w; } // int matrix^2 (be careful about negative value) public static int[][] p2(int[][] A) { int n = A.length; int[][] C = new int[n][n]; for(int i = 0;i < n;i++){ long[] sum = new long[n]; for(int k = 0;k < n;k++){ for(int j = 0;j < n;j++){ sum[j] += (long)A[i][k] * A[k][j]; if(sum[j] >= BIG)sum[j] -= BIG; } } for(int j = 0;j < n;j++){ C[i][j] = (int)(sum[j] % mod); } } return C; } //////////// end // ret[n]=A^(2^n) public static int[][][] generateP2(int[][] A, int n) { int[][][] ret = new int[n+1][][]; ret[0] = A; for(int i = 1;i <= n;i++)ret[i] = p2(ret[i-1]); return ret; } // A[0]^e*v // A[n]=A[0]^(2^n) public static int[] pow(int[][][] A, int[] v, long e) { for(int i = 0;e > 0;e>>>=1,i++) { if((e&1)==1)v = mul(A[i], v); } return v; } public static int[][] mul(int[][]... a) { int[][] base = a[0]; for(int i = 1;i < a.length;i++){ base = mul(base, a[i]); } return base; } // メモ累乗計算セット ここまで // A^e // O(N^3log N) public static int[][] pow(int[][] A, long e) { int[][] MUL = A; int n = A.length; int[][] C = new int[n][n]; for(int i = 0;i < n;i++)C[i][i] = 1; for(;e > 0;e>>>=1) { if((e&1)==1)C = mul(C, MUL); MUL = p2(MUL); } return C; } public static int[][] mul(int[][] A, int[][] B) { assert A[0].length == B.length; int m = A.length; int n = A[0].length; int o = B[0].length; int[][] C = new int[m][o]; for(int i = 0;i < m;i++){ long[] sum = new long[o]; for(int k = 0;k < n;k++){ for(int j = 0;j < o;j++){ sum[j] += (long)A[i][k] * B[k][j]; if(sum[j] >= BIG)sum[j] -= BIG; } } for(int j = 0;j < o;j++){ C[i][j] = (int)(sum[j] % mod); } } return C; } 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 C().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)); } }