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Problem W1.4 (Bzout's identity and certifying Euclidean algorithm). An algorithm is called certifying when it can check whether the output is correct or not. For ex- ample, the highest common factor h of two integers n and m, not simultaneously 0, is characterised by being a divisor of both and writable in the form h=sm+tn for some stez. (W1.4.1) The latter is called Bzout's identity. The extended Euclidean algorithm provides a construction of such coefficients set as follows Require: m,n two integers with n=0 Ensure: r,s,t integers such that r=hcf{m, n} and sm+tn=r (Bzout) 1: procedure EXTENDED-EUCLID(m,n) r-1 m, ron , k- 1 while re #0 do answer is reached when rk = 0 (9k, rk) - div{rk-2, Pk-1) (sk, tk) - (Sk-1, tk-1)-9(Sk-2, tk-2) krk+1 7: end while 8: return Ik-1 phcf is the last non-zero remainder 9: end procedure Write a code that inputs two integers m, n, not simultaneously zero, and outputs three integers r, s, t such that r=hcf{m, n} and h=sm+tn. [40 marks] i Problem W1.4 (Bzout's identity and certifying Euclidean algorithm). An algorithm is called certifying when it can check whether the output is correct or not. For ex- ample, the highest common factor h of two integers n and m, not simultaneously 0, is characterised by being a divisor of both and writable in the form h=sm+tn for some stez. (W1.4.1) The latter is called Bzout's identity. The extended Euclidean algorithm provides a construction of such coefficients set as follows Require: m,n two integers with n=0 Ensure: r,s,t integers such that r=hcf{m, n} and sm+tn=r (Bzout) 1: procedure EXTENDED-EUCLID(m,n) r-1 m, ron , k- 1 while re #0 do answer is reached when rk = 0 (9k, rk) - div{rk-2, Pk-1) (sk, tk) - (Sk-1, tk-1)-9(Sk-2, tk-2) krk+1 7: end while 8: return Ik-1 phcf is the last non-zero remainder 9: end procedure Write a code that inputs two integers m, n, not simultaneously zero, and outputs three integers r, s, t such that r=hcf{m, n} and h=sm+tn. [40 marks]