From aa2bbbb1ae9aec141160a875643d86a00a8695dc Mon Sep 17 00:00:00 2001
From: Adil Nawaz <36169021+adilnawaz113@users.noreply.github.com>
Date: Fri, 11 Oct 2019 00:06:44 +0530
Subject: [PATCH] fiboSum

---
 data_structures/fiboSum.cpp | 53 +++++++++++++++++++++++++++++++++++++
 1 file changed, 53 insertions(+)
 create mode 100644 data_structures/fiboSum.cpp

diff --git a/data_structures/fiboSum.cpp b/data_structures/fiboSum.cpp
new file mode 100644
index 0000000..7256dbb
--- /dev/null
+++ b/data_structures/fiboSum.cpp
@@ -0,0 +1,53 @@
+  
+// https://www.spoj.com/problems/FIBOSUM/
+// sum=fibo(m+2)-fibo(n+1), here answer can be negative, so be careful.
+// https://codegeeksblog.wordpress.com/2013/06/02/spoj-fibosum/
+
+// To find nth fibonacci number in log(n) time please see below concepts.
+// See this link https://cp-algorithms.com/algebra/binary-exp.html
+// https://cp-algorithms.com/algebra/fibonacci-numbers.html
+// Video https://www.youtube.com/watch?v=EEb6JP3NXBI
+#include <bits/stdc++.h>
+using namespace std;
+long long MAX = 1000000007;
+void multiply(long long F[2][2], long long M[2][2])
+{
+    long long w = ((F[0][0] * M[0][0]) % MAX + (F[0][1] * M[1][0]) % MAX) % MAX;
+    long long x = ((F[0][0] * M[0][1]) % MAX + (F[0][1] * M[1][1]) % MAX) % MAX;
+    long long y = ((F[1][0] * M[0][0]) % MAX + (F[1][1] * M[1][0]) % MAX) % MAX;
+    long long z = ((F[1][0] * M[0][1]) % MAX + (F[1][1] * M[1][1]) % MAX) % MAX;
+    F[0][0] = w;
+    F[0][1] = x;
+    F[1][0] = y;
+    F[1][1] = z;
+}
+void power(long long F[2][2], long long n)
+{
+    if (n == 0 || n == 1)
+        return;
+    long long M[2][2] = {{1, 1}, {1, 0}};
+    power(F, n / 2);
+    multiply(F, F);
+    if (n & 1)
+        multiply(F, M);
+}
+long long fibo(long long n)
+{
+    long long F[2][2] = {{1, 1}, {1, 0}};
+    if (n == 0)
+        return 0;
+    power(F, n - 1);
+    return F[0][0];
+}
+int main()
+{
+    long long t, n, m;
+    cin >> t;
+    while (t--)
+    {
+        cin >> m >> n;
+        // Here added MAX because to remove negative sign.
+        cout << (fibo(n + 2) - fibo((m - 1) + 2) + MAX) % MAX << endl;
+    }
+    return 0;
+}