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| 1 | +//SPOJ |
| 2 | +/* |
| 3 | +* |
| 4 | +* INTERESTING FORMULA LEARNED |
| 5 | +* BINET'S FORMULA FOR SUM OF A RANGE OF FIBONACCI NUMBERS |
| 6 | +* |
| 7 | +* S(N) = F(N+2) - 1 ; |
| 8 | +* |
| 9 | +* AND |
| 10 | +* |
| 11 | +* S(L,R) = F(R+2) - F(L+1) ; |
| 12 | +* |
| 13 | +* |
| 14 | +* |
| 15 | +* |
| 16 | +* */ |
| 17 | + |
| 18 | +import java.io.*; |
| 19 | + |
| 20 | +public class FIBOSUM { |
| 21 | + |
| 22 | + static long MOD = 1000000007; |
| 23 | + public static void main(String[] args)throws IOException { |
| 24 | + BufferedReader br = new BufferedReader(new InputStreamReader(System.in)); |
| 25 | + |
| 26 | + int t = Integer.parseInt(br.readLine()); |
| 27 | + while(t-- > 0) { |
| 28 | + String[] s = br.readLine().split(" "); |
| 29 | + long n = Long.parseLong(s[0]); |
| 30 | + long m = Long.parseLong(s[1]); |
| 31 | + m+=2; |
| 32 | + n+=1; |
| 33 | + |
| 34 | + |
| 35 | + m--; |
| 36 | + long[][] M = {{1,1},{1,0}}; |
| 37 | + long[][] IdentityM = {{1,0},{0,1}}; |
| 38 | + |
| 39 | + while(m > 0){ |
| 40 | + if((m & 1) == 1){ |
| 41 | + IdentityM = multiply(IdentityM,M); |
| 42 | + } |
| 43 | + M = multiply(M,M); |
| 44 | + m = m >> 1; |
| 45 | + } |
| 46 | + |
| 47 | + long ansM = (IdentityM[0][0])%MOD; |
| 48 | + |
| 49 | + n--; |
| 50 | + long[][] N = {{1,1},{1,0}}; |
| 51 | + long[][] IdentityN = {{1,0},{0,1}}; |
| 52 | + |
| 53 | + while(n > 0){ |
| 54 | + if((n & 1) == 1){ |
| 55 | + IdentityN = multiply(IdentityN,N); |
| 56 | + } |
| 57 | + N = multiply(N,N); |
| 58 | + n = n >> 1; |
| 59 | + } |
| 60 | + |
| 61 | + long ansN = (IdentityN[0][0])%MOD; |
| 62 | + long sum = (ansM - ansN + MOD)%MOD; |
| 63 | + |
| 64 | + System.out.println(sum); |
| 65 | + |
| 66 | + } |
| 67 | + } |
| 68 | + |
| 69 | + private static long[][] multiply(long[][] A,long[][] B){ |
| 70 | + long a = (A[0][0]*B[0][0] + A[0][1]*B[1][0])%MOD; |
| 71 | + long b = (A[0][0]*B[0][1] + A[0][1]*B[1][1])%MOD; |
| 72 | + long c = (A[1][0]*B[0][0] + A[1][1]*B[1][0])%MOD; |
| 73 | + long d = (A[1][0]*B[0][1] + A[1][1]*B[1][1])%MOD; |
| 74 | + |
| 75 | + A[0][0] = a; |
| 76 | + A[0][1] = b; |
| 77 | + A[1][0] = c; |
| 78 | + A[1][1] = d; |
| 79 | + |
| 80 | + return A; |
| 81 | + } |
| 82 | +} |
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